{"id":31198,"date":"2021-03-28T13:00:14","date_gmt":"2021-03-28T13:00:14","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=31198"},"modified":"2025-01-12T13:22:07","modified_gmt":"2025-01-12T13:22:07","slug":"%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/","title":{"rendered":"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\t\ttext-align: center;\n\t}\n<\/style>\n<h1>\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629<\/h1>\n<p style=\"text-align:center;\">\n\t<em><br \/>\n\t\u0643\u0645 \u0639\u062f\u062f \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0644\u062a\u0631\u062a\u064a\u0628 \u0646\u0638\u0627\u0645 \u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0645\u0643\u0648\u0646 \u0645\u0646 \u0645\u0644\u0627\u064a\u064a\u0646 \u0627\u0644\u0639\u0646\u0627\u0635\u0631\u061f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u0646\u0627\u0642\u0634 \u0643\u064a\u0641 \u062a\u064f\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0645\u0646 \u0627\u0644\u0625\u062c\u0627\u0628\u0629 \u0639\u0644\u0649 \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0641\u064a \u0633\u064a\u0627\u0642 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\u060c \u0628\u062f\u0621\u064b\u0627 \u0645\u0646 \u062a\u0648\u0632\u064a\u0639 \u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0637\u0627\u0642\u0629 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0630\u0631\u064a\u0629 \u0648\u062d\u062a\u0649 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0643\u0648\u064a\u0646\u0627\u062a \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0630\u0627\u062a \u0627\u0644\u0646\u0637\u0627\u0642 \u0627\u0644\u0643\u0628\u064a\u0631. \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0623\u062f\u0648\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629\u060c \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a\u060c \u0633\u0646\u0633\u062a\u0643\u0634\u0641 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u062c\u062f\u064b\u0627 \u0648\u062d\u0644 \u0645\u0634\u0627\u0643\u0644 \u062a\u0628\u062f\u0648 \u0645\u0633\u062a\u0639\u0635\u064a\u0629.<br \/>\n\t<\/em>\n<\/p>\n<p style=\"text-align:center;\">\n\t<strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n\t\u0639\u0646\u062f \u0627\u0646\u062a\u0647\u0627\u0621 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u062a\u0645\u0643\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0645\u0646:\n<\/p>\n<ol>\n<li><strong>\u0641\u0647\u0645<\/strong> \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0633\u064a\u0627\u0642 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\u060c \u0644\u0627 \u0633\u064a\u0645\u0627 \u0641\u064a \u062a\u0646\u0638\u064a\u0645 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629.<\/li>\n<li><strong>\u062d\u0633\u0627\u0628<\/strong> \u0627\u0644\u062a\u0643\u0648\u064a\u0646\u0627\u062a \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0644\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0630\u0631\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0644\u062a\u0642\u062f\u064a\u0631 \u0631\u062a\u0628\u0629 \u0627\u0644\u062d\u062c\u0645 \u0644\u0644\u062a\u0643\u0648\u064a\u0646\u0627\u062a \u0627\u0644\u0645\u0639\u0642\u062f\u0629.<\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n\t<u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a:<\/u><br \/>\n\t<a href=\"#1\"><strong>\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629<\/strong><\/a><br \/>\n\t<a href=\"#2\"><strong>\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/strong><\/a><br \/>\n\t<a href=\"#3\">\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0644\u062d\u0633\u0627\u0628 \u0631\u062a\u0628\u0629 \u0627\u0644\u062d\u062c\u0645<\/a><br \/>\n\t<a href=\"#4\"><em>\u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0645\u0628\u0633\u0637<\/em><\/a><br \/>\n\t<a href=\"#5\"><em>\u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0639\u0627\u062f\u064a<\/em><\/a><br \/>\n\t<a href=\"#6\"><strong>\u0623\u0645\u062b\u0644\u0629 \u0639\u0646 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u062a\u0642\u062f\u064a\u0631 \u0631\u062a\u0628\u0629 \u0627\u0644\u062d\u062c\u0645<\/strong><\/a><br \/>\n\t<a href=\"#7\">\u0627\u0644\u062d\u0627\u0644\u0629 1: \u0627\u0644\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/a><br \/>\n\t<a href=\"#8\">\u0627\u0644\u062d\u0627\u0644\u0629 2: \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/a>\n<\/p>\n<p>\n\t\u0633\u0624\u0627\u0644 \u0634\u0627\u0626\u0639 \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629 \u0647\u0648: \u0643\u0645 \u0639\u062f\u062f \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 \u062a\u0631\u062a\u064a\u0628 \u0646\u0638\u0627\u0645 \u0645\u0639\u064a\u0646\u061f \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0634\u0627\u0626\u0639\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629. \u0648\u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646\u0647\u0627 \u062a\u0628\u062f\u0648 \u0628\u0633\u064a\u0637\u0629 \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629\u060c \u0625\u0644\u0627 \u0623\u0646\u0647\u0627 \u062a\u0635\u0628\u062d \u0645\u0639\u0642\u062f\u0629 \u0639\u0646\u062f \u0625\u062f\u0631\u0627\u062c \u0623\u0631\u0642\u0627\u0645 \u0643\u0628\u064a\u0631\u0629 \u062c\u062f\u064b\u0627\u060c \u0645\u062b\u0644 <strong><a href=\"http:\/\/toposuranos.com\/material\/mol-y-masa-molar\/\" rel=\"noopener\" target=\"_blank\">\u0639\u062f\u062f \u0623\u0641\u0648\u062c\u0627\u062f\u0631\u0648<\/a><\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N_A<\/span><\/span>\u060c \u0645\u0645\u0627 \u064a\u064f\u0628\u0631\u0632 \u0635\u0639\u0648\u0628\u0629 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0647\u0627\u0626\u0644\u0629.\n<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629<\/h2>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/K7_De9wux4A?si=q93_T8xh15EdfJ6B\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p>\n\t\u0644\u0641\u0647\u0645 \u0645\u062f\u0649 \u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u064a \u062a\u0646\u0637\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0623\u062e\u0630 \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a:\n<\/p>\n<h4>\u0645\u062b\u0627\u0644: \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0639\u0644\u0649 \u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0637\u0627\u0642\u0629<\/h4>\n<p>\n\t\u0644\u0646\u0641\u062a\u0631\u0636 \u0648\u062c\u0648\u062f \u0646\u0638\u0627\u0645 \u0645\u0643\u0648\u0646 \u0645\u0646 10 \u0630\u0631\u0627\u062a. \u064a\u0645\u0643\u0646 \u0644\u0643\u0644 \u0630\u0631\u0629 \u062a\u062e\u0632\u064a\u0646 1 \u0623\u0648 0 \u0648\u062d\u062f\u0629 \u0645\u0646 \u0627\u0644\u0637\u0627\u0642\u0629\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u064f\u0633\u0645\u0649 <strong>\u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0637\u0627\u0642\u0629<\/strong>. \u0643\u0645 \u0639\u062f\u062f \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 \u062a\u0648\u0632\u064a\u0639 \u0647\u0630\u0647 \u0627\u0644\u0643\u0645\u064a\u0627\u062a \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 (\u0623) 10 \u0643\u0645\u064a\u0627\u062a \u0637\u0627\u0642\u0629 \u0648(\u0628) 5 \u0643\u0645\u064a\u0627\u062a \u0637\u0627\u0642\u0629\u061f\n<\/p>\n<h5>\u0627\u0644\u062d\u0644<\/h5>\n<p>\n\t\u0646\u064f\u0645\u062b\u0644 \u0627\u0644\u0630\u0631\u0627\u062a \u0643\u0623\u0645\u0627\u0643\u0646 \u0645\u062a\u0627\u062d\u0629 \u0644\u062a\u062e\u0632\u064a\u0646 \u0643\u0645\u064a\u0629 \u0637\u0627\u0642\u0629 \u0648\u0627\u062d\u062f\u0629. \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0643\u0627\u0646 \u0645\u0645\u062a\u0644\u0626\u064b\u0627\u060c \u0641\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0627\u0644\u0630\u0631\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u062a\u0645\u062a\u0644\u0643 \u0643\u0645\u064a\u0629 \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0647\u0627.\n<\/p>\n<p><center><br \/>\n\t<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-zJa7H7iMOGY\/YF3QhG94SoI\/AAAAAAAAEuI\/olfdSHfeJOgKea3vHXEAyr5QCJ1ZjmcpgCLcBGAsYHQ\/s839\/cuantodeenergia.PNG\" class=\"aligncenter lazyload\" alt=\"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\" width=\"400\" height=\"200\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-zJa7H7iMOGY\/YF3QhG94SoI\/AAAAAAAAEuI\/olfdSHfeJOgKea3vHXEAyr5QCJ1ZjmcpgCLcBGAsYHQ\/s839\/cuantodeenergia.PNG\" class=\"aligncenter lazyload\" alt=\"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\" width=\"400\" height=\"200\" \/><\/noscript><br \/>\n<\/center><\/p>\n<p>\n\t\u0644\u062d\u0633\u0627\u0628 \u0639\u062f\u062f \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0628\u0647\u0627 \u062a\u0648\u0632\u064a\u0639 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0643\u0645\u064a\u0627\u062a \u0637\u0627\u0642\u0629 \u0628\u064a\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0623\u0645\u0627\u0643\u0646\u060c \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\binom{n}{k}=\\dfrac{n!}{k!(n-k)!}<\/span><\/span>\n<\/p>\n<p>\n\t\u0647\u0630\u0627 \u0627\u0644\u062d\u0633\u0627\u0628 \u064a\u0639\u0637\u064a\u0646\u0627 \u0627\u0644\u0639\u062f\u062f <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> \u0644\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u0645\u0643\u0646\u0629.\n<\/p>\n<p>\n\t<strong>(\u0623)<\/strong> \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0647\u0646\u0627\u0643 10 \u0643\u0645\u064a\u0627\u062a \u0645\u0648\u0632\u0639\u0629 \u0628\u064a\u0646 10 \u0623\u0645\u0627\u0643\u0646\u060c \u0641\u0647\u0646\u0627\u0643 \u0637\u0631\u064a\u0642\u0629 \u0648\u0627\u062d\u062f\u0629 \u0641\u0642\u0637 \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega=1<\/span><\/span>:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\Omega = \\binom{10}{10}=\\dfrac{10!}{10!(10-10)!} = \\dfrac{10!}{10!0!} = 1 <\/span><\/span>\n<\/p>\n<p>\n\t<strong>(\u0628)<\/strong> \u0644\u062a\u0648\u0632\u064a\u0639 5 \u0643\u0645\u064a\u0627\u062a \u0628\u064a\u0646 10 \u0623\u0645\u0627\u0643\u0646\u060c \u0646\u0642\u0648\u0645 \u0628\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0627\u0644\u064a:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\t\\Omega &amp;= \\displaystyle\\binom{10}{5} \\\\ \\\\\n\n\t&amp;=\\dfrac{10!}{5!(10-5)!} = \\dfrac{10!}{5!\\cdot 5!} \\\\ \\\\\n\n\t&amp;= \\dfrac{5! \\cdot 6\\cdot 7\\cdot 8 \\cdot 9\\cdot 10}{5! \\cdot 2\\cdot 3\\cdot 4\\cdot 5} \\\\ \\\\\n\n\t&amp;= \\dfrac{ 7\\cdot 8 \\cdot 9\\cdot 10}{ 4\\cdot 5} = 7\\cdot 2 \\cdot 9 \\cdot 2 = 252\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\n\t\u0644\u0630\u0644\u0643\u060c \u0647\u0646\u0627\u0643 252 \u062a\u0643\u0648\u064a\u0646\u064b\u0627 \u0645\u0645\u0643\u0646\u064b\u0627.\n<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/h2>\n<p>\n\t\u0645\u0627 \u0642\u0645\u0646\u0627 \u0628\u062a\u062d\u0644\u064a\u0644\u0647 \u062d\u062a\u0649 \u0627\u0644\u0622\u0646 \u0647\u0648 \u0645\u062c\u0631\u062f \u0627\u0644\u0628\u062f\u0627\u064a\u0629. \u0625\u0630\u0627 \u0642\u0645\u0646\u0627 \u0628\u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0646\u0638\u0627\u0645 \u0641\u064a \u0627\u0644\u062d\u0627\u0644\u0629 (\u0628) \u0644\u064a\u0634\u0645\u0644 100 \u0630\u0631\u0629 \u064850 \u0643\u0645\u064a\u0629 \u0637\u0627\u0642\u0629\u060c \u0633\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega \\approx 10^{28}<\/span><\/span>. \u0627\u0644\u0622\u0646\u060c \u062a\u062e\u064a\u0644 \u0625\u062c\u0631\u0627\u0621 \u0646\u0641\u0633 \u0627\u0644\u062d\u0633\u0627\u0628 \u0645\u0639 \u0645\u0648\u0644 \u0648\u0627\u062d\u062f \u0645\u0646 \u0627\u0644\u0630\u0631\u0627\u062a\u061b \u0633\u062a\u0643\u0648\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0644\u0627 \u064a\u0645\u0643\u0646 \u062a\u0635\u0648\u0631\u0647\u0627.\n<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0644\u062d\u0633\u0627\u0628 \u0631\u062a\u0628\u0629 \u0627\u0644\u062d\u062c\u0645<\/h3>\n<p>\n\t\u0639\u0646\u062f\u0645\u0627 \u0646\u0631\u063a\u0628 \u0641\u064a \u062a\u0642\u062f\u064a\u0631 \u0645\u0642\u062f\u0627\u0631 \u0645\u0646 \u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega = \\binom{n}{k}<\/span><\/span> \u0644\u0642\u064a\u0645 \u0643\u0628\u064a\u0631\u0629 \u0644\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>\u060c \u062e\u0627\u0635\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span><\/span>\u060c \u0648\u0647\u064a \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u0635\u0644 \u0641\u064a\u0647\u0627 \u0627\u0644\u0642\u064a\u0645 \u0625\u0644\u0649 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0642\u0635\u0649\u060c \u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0645\u0641\u064a\u062f \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a \u0644\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a.\n<\/p>\n<p>\n\t\u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0628\u0647\u0630\u0627 \u0627\u0644\u062d\u062c\u0645\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u0639\u0627\u062f\u0629 \u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0628\u0623\u062e\u0630 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a\u060c \u0648\u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\ln(\\Omega)=\\ln\\left(\\dfrac{n!}{k!(n-k)!}\\right)= \\ln(n!) - \\ln((n-k)!) - \\ln(k!)<\/span><\/span>\n<\/p>\n<p>\n\t\u064a\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637 \u0647\u0630\u0647 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u062e\u0627\u0635 \u0628\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0639\u0627\u0645\u0644\u060c \u062d\u064a\u062b \u0644\u062f\u064a\u0646\u0627 \u0646\u0633\u062e\u062a\u0627\u0646 \u0645\u0645\u0643\u0646\u062a\u0627\u0646: \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0648\u0627\u0644\u0645\u0628\u0633\u0637\u0629.\n<\/p>\n<ul>\n<li>\n\t\t<strong>\u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0639\u0627\u062f\u064a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(n!) \\approx \\dfrac{1}{2}\\ln(2n\\pi) + n\\ln(n) - n<\/span><\/span>\n\t<\/li>\n<li>\n\t\t<strong>\u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0645\u0628\u0633\u0637:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(n!) \\approx  n\\ln(n) - n<\/span><\/span>\n\t<\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/p>\n<h4>\u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0645\u0628\u0633\u0637<\/h4>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/fnt99FeeHPM?si=H6r-5GhO2yqaeaXd\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p>\n\t\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0645\u0628\u0633\u0637 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u0627\u0644\u064a\u0629:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\t\\ln(\\Omega) &amp; \\approx n\\ln(n) - n - (n-k)\\ln(n-k) + (n-k) - k\\ln(k) + k \\\\ \\\\\n\n\t&amp;= n\\ln(n) - (n-k)\\ln(n-k) - k\\ln(k) \\\\ \\\\\n\n\t&amp;= n\\ln(n) - n\\ln(n-k) + k\\ln(n-k) - k\\ln(k) \\\\ \\\\\n\n\t&amp;= \\ln\\left[ \\left( \\dfrac{n}{n-k} \\right)^n \\right] + k\\ln\\left( \\dfrac{n-k}{k} \\right) \\\\ \\\\\n\n\t&amp;= \\ln\\left[ \\dfrac{1}{\\left(1 - \\dfrac{k}{n} \\right)^n} \\right] + k\\ln\\left( \\dfrac{n}{k} - 1 \\right)\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\n\t\u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u064a\u0623\u062e\u0630 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0644\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>\u060c \u0646\u0637\u0628\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{n\\to\\infty} \\left(1-\\dfrac{k}{n} \\right)^n = e^{-k} <\/span><\/span>\n<\/p>\n<p>\n\t\u0628\u0627\u0644\u062a\u0627\u0644\u064a:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(\\Omega) \\approx \\ln(e^k) + k\\ln\\left( \\dfrac{n}{k} -1 \\right) = k + k\\ln\\left( \\dfrac{n}{k} -1 \\right) <\/span><\/span>\n<\/p>\n<p>\n\t\u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u062d\u0648\u064a\u0644 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\log(\\Omega) = \\log(e)\\ln(\\Omega) \\approx k\\log(e)\\left[1 + \\ln\\left( \\dfrac{n}{k} - 1 \\right) \\right] <\/span><\/span>\n<\/p>\n<p>\n\t\u0645\u0645\u0627 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0627\u0644\u0646\u062a\u064a\u062c\u0629:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\Omega \\approx 10^{k\\log(e)\\left[1 + \\ln\\left( \\dfrac{n}{k} - 1 \\right) \\right]}}<\/span><\/span>\n<\/p>\n<p>\n\t\u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0644\u0627 \u062a\u0639\u0637\u064a \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062f\u0642\u064a\u0642\u0629 \u0644\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span>\u060c \u0625\u0644\u0627 \u0623\u0646\u0647\u0627 \u062a\u0633\u0645\u062d \u0628\u062a\u0642\u062f\u064a\u0631 \u0639\u062f\u062f \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u062a\u0645\u062b\u064a\u0644\u0647\u060c \u0648\u062a\u062a\u062d\u0633\u0646 \u0627\u0644\u062f\u0642\u0629 \u0645\u0639 \u0632\u064a\u0627\u062f\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>.\n<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h4>\u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0639\u0627\u062f\u064a<\/h4>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/i3OO4lHV24Q?si=jEPCafXqgVxNYqH-\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p>\n\t\u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0639\u0627\u062f\u064a \u064a\u0648\u0641\u0631 \u0646\u062a\u064a\u062c\u0629 \u0623\u0643\u062b\u0631 \u062f\u0642\u0629\u060c \u0625\u0644\u0627 \u0623\u0646\u0647 \u064a\u062a\u0636\u0645\u0646 \u0628\u0639\u0636 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0625\u0636\u0627\u0641\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0624\u062f\u064a \u0625\u0644\u0649 \u0646\u062a\u0627\u0626\u062c \u0645\u0643\u0627\u0641\u0626\u0629 \u062a\u0642\u0631\u064a\u0628\u064b\u0627 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0644\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>. \u064a\u0634\u062a\u0631\u0643 \u0647\u0630\u0627 \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0645\u062a \u0628\u0627\u0644\u0641\u0639\u0644 \u0641\u064a \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0645\u0628\u0633\u0637\u060c \u0648\u064a\u062a\u0644\u062e\u0635 \u0641\u064a \u0627\u0644\u0645\u0646\u0647\u062c\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\t\\ln(\\Omega) &amp; = &amp; \\ln\\left(\\dfrac{n!}{k!(n-k)!}\\right)= \\ln(n!) - \\ln((n-k)!) - \\ln(k!) \\\\ \\\\\n\n\t&amp; \\approx &amp; \\color{red}\\dfrac{1}{2}\\ln(2n\\pi)\\color{black} + n\\ln(n) - n \\\\ \\\\\n\n\t&amp; &amp; \\color{red}-\\dfrac{1}{2}\\ln(2(n-k)\\pi)\\color{black} - (n-k)\\ln(n-k) + (n-k) \\\\ \\\\\n\n\t&amp; &amp; \\color{red}-\\dfrac{1}{2}\\ln(2k\\pi)\\color{black} - k\\ln(k) + k\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\n\t\u062a\u0634\u064a\u0631 \u0627\u0644\u0623\u062c\u0632\u0627\u0621 \u0627\u0644\u0645\u0645\u064a\u0632\u0629 \u0628\u0627\u0644\u0644\u0648\u0646 \u0627\u0644\u0623\u062d\u0645\u0631 \u0625\u0644\u0649 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0625\u0636\u0627\u0641\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u064f\u0636\u0627\u0641 \u0641\u064a \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0639\u0627\u062f\u064a\u060c \u0628\u064a\u0646\u0645\u0627 \u062a\u0645\u062b\u0644 \u0627\u0644\u0623\u062c\u0632\u0627\u0621 \u0627\u0644\u0623\u062e\u0631\u0649 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0628\u0627\u0644\u0641\u0639\u0644 \u0641\u064a \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0645\u0628\u0633\u0637. \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0630\u0644\u0643 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\t\\ln(\\Omega) &amp; \\approx &amp; \\color{red}\\dfrac{1}{2}\\ln\\left( \\dfrac{2n\\pi}{2(n-k)\\pi \\cdot 2k\\pi} \\right)\\color{black} + k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) \\\\ \\\\\n\n\t&amp; = &amp;  k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2k\\pi(n-k)}{n}\\right)\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\n\t\u062b\u0645\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u062d\u0648\u064a\u0644 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\log(\\Omega) = \\log(e)\\ln(\\Omega) \\approx \\log(e) \\left[ k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2k\\pi(n-k)}{n}\\right) \\right] <\/span><\/span>\n<\/p>\n<p>\n\t\u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0623\u0633 \u0627\u0644\u0623\u0633\u0627\u0633 10 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\Omega \\approx 10^{\\log(e) \\left[ k + k\\ln\\left(\\dfrac{n}{k} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2k\\pi(n-k)}{n}\\right) \\right]}<\/span>\n<\/p>\n<p>\n\t\u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u064a\u0636\u064b\u0627\u060c \u0643\u0645\u0627 \u0641\u064a \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0642\u0635\u0648\u0649 \u0644\u0647\u0630\u0627 \u0627\u0644\u0639\u062f\u062f \u0628\u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u062d\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span><\/span>\u060c \u0645\u0645\u0627 \u064a\u0648\u0641\u0631 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\t\\text{Max}(\\Omega) &amp;\\approx &amp; 10^{\\log(e) \\left[ \\dfrac{n}{2} + \\dfrac{n}{2}\\ln\\left(\\dfrac{n}{(n\/2)} - 1\\right) - \\dfrac{1}{2}\\ln\\left(\\dfrac{2(n\/2)\\pi(n-n\/2)}{n}\\right) \\right]} \\\\ \\\\\n\n\t&amp; = &amp; 10^{\\log(e) \\left[\\dfrac{n}{2} - \\dfrac{1}{2}\\ln\\left(\\dfrac{n\\pi}{2} \\right) \\right]} = 10^{\\log(e)(n-\\ln(n\\pi\/2))\/2}\n\n\t\\end{array}<\/span>\n<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u0623\u0645\u062b\u0644\u0629 \u0639\u0646 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u062a\u0642\u062f\u064a\u0631 \u0631\u062a\u0628\u0629 \u0627\u0644\u062d\u062c\u0645<\/h2>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/M7NrtICrSzU?si=6UT34333Wp5YwFU1\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u0627\u0644\u062d\u0627\u0644\u0629 1: \u0627\u0644\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/h3>\n<p>\n\t\u0644\u0646\u0642\u062f\u0631 \u0631\u062a\u0628\u0629 \u0627\u0644\u062d\u062c\u0645 \u0644\u0640 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(10^{50}\\right)!<\/span><\/span>\u060c \u0623\u064a \u0639\u062f\u062f \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u0643\u062a\u0627\u0628\u0629 \u0647\u0630\u0627 \u0627\u0644\u0639\u062f\u062f.\n<\/p>\n<h5>\u0627\u0644\u062d\u0644<\/h5>\n<p>\n\t\u0644\u062d\u0633\u0627\u0628 \u0647\u0630\u0627\u060c \u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0628\u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\n\t\\begin{array}{rl}\n\n\t\\ln\\left[ \\left(10^{50}\\right)! \\right] &amp;\\approx 10^{50}\\ln\\left(10^{50}\\right) - 10^{50}\\\\ \\\\\n\n\t&amp;= \\left[\\ln\\left(10^{50}\\right) -1\\right]10^{50}  \\\\ \\\\\n\n\t&amp;= \\left[50\\ln(10)-1 \\right]10^{50} \\\\ \\\\\n\n\t\\end{array}\n\n\t<\/span>\n<\/p>\n<p>\n\t\u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0646\u0637\u0628\u0642 \u062a\u062d\u0648\u064a\u0644 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\ln\\left[ \\left(10^{50}\\right)! \\right] = \\dfrac{\\log\\left[\\left(10^{50}\\right)!\\right]}{\\log{e}}<\/span>\n<\/p>\n<p>\n\t\u0628\u0627\u0644\u062a\u0627\u0644\u064a:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\log\\left[ \\left(10^{50}\\right)! \\right] \\approx \\log(e)\\left[50\\ln(10)-1 \\right]10^{50}<\/span>\n<\/p>\n<p>\n\t\u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0628\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0623\u0633 \u0627\u0644\u0623\u0633\u0627\u0633 10\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\left(10^{50}\\right)!  \\approx  10^{\\log(e)\\left[50\\ln(10)-1 \\right]10^{50}} = 10^{49,5657 \\cdot 10^{50}}<\/span>\n<\/p>\n<p>\n\t\u064a\u0645\u062b\u0644 \u0627\u0644\u0623\u0633 \u0641\u0648\u0642 \u0627\u0644\u0639\u062f\u062f 10 \u0631\u062a\u0628\u0629 \u0627\u0644\u062d\u062c\u0645\u060c \u0645\u0645\u0627 \u064a\u0648\u0641\u0631 \u062a\u0642\u062f\u064a\u0631\u064b\u0627 \u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u062a\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u064a\u0647\u0627 \u0627\u0644\u0639\u062f\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(10^{50}\\right)!<\/span><\/span>.\n<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<h3>\u0627\u0644\u062d\u0627\u0644\u0629 2: \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/h3>\n<p>\n\t\u0641\u064a \u0645\u0646\u0632\u0644 \u0639\u0627\u062f\u064a \u064a\u0648\u062c\u062f \u062a\u0642\u0631\u064a\u0628\u064b\u0627 12 \u0645\u0641\u062a\u0627\u062d \u0625\u0636\u0627\u0621\u0629\u060c \u0648\u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0643\u0644 \u0645\u0641\u062a\u0627\u062d \u0641\u064a \u0648\u0636\u0639 \u0627\u0644\u062a\u0634\u063a\u064a\u0644 \u0623\u0648 \u0627\u0644\u0625\u064a\u0642\u0627\u0641. \u0641\u064a \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u060c \u064a\u0633\u0643\u0646 \u0643\u0644 \u0645\u0646\u0632\u0644 4 \u0623\u0634\u062e\u0627\u0635. \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 5 \u0645\u0644\u0627\u064a\u064a\u0646 \u0646\u0633\u0645\u0629 \u0641\u064a \u0645\u062f\u064a\u0646\u0629\u060c \u0643\u0645 \u0639\u062f\u062f \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0646\u0635\u0641 \u0645\u0641\u0627\u062a\u064a\u062d \u0627\u0644\u0625\u0636\u0627\u0621\u0629 \u0641\u064a \u0627\u0644\u0645\u062f\u064a\u0646\u0629 \u0642\u064a\u062f \u0627\u0644\u062a\u0634\u063a\u064a\u0644\u061f\n<\/p>\n<h5>\u0627\u0644\u062d\u0644<\/h5>\n<p>\n\t\u0639\u062f\u062f \u0627\u0644\u0645\u0641\u0627\u062a\u064a\u062d <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0641\u064a \u0627\u0644\u0645\u062f\u064a\u0646\u0629:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\n\t\\begin{array}{rcl}\n\n\tn &amp;=&amp;\\dfrac{\\text{\u0639\u062f\u062f \u0633\u0643\u0627\u0646 \u0627\u0644\u0645\u062f\u064a\u0646\u0629}}{\\text{\u0639\u062f\u062f \u0627\u0644\u0623\u0634\u062e\u0627\u0635 \u0641\u064a \u0627\u0644\u0645\u0646\u0632\u0644}} \\times \\text{\u0639\u062f\u062f \u0627\u0644\u0645\u0641\u0627\u062a\u064a\u062d \u0644\u0643\u0644 \u0645\u0646\u0632\u0644} \\\\ \\\\\n\n\t&amp;=&amp; \\dfrac{5\\cdot 10^6}{4}\\cdot 12 = 15\\cdot 10^6\n\n\t\\end{array}\n\n\t<\/span>\n<\/p>\n<p>\n\t\u064a\u064f\u0634\u0643\u0644 \u0627\u0644\u0645\u0627\u0643\u0631\u0648\u0633\u062a\u064a\u062a \u0627\u0644\u0645\u0643\u0648\u0646 \u0645\u0646 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u064a\u0643\u0631\u0648\u0633\u062a\u064a\u062a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0646\u0635\u0641 \u0627\u0644\u0645\u0641\u0627\u062a\u064a\u062d \u0642\u064a\u062f \u0627\u0644\u062a\u0634\u063a\u064a\u0644 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u062a\u064a \u0644\u062f\u064a\u0647\u0627 \u0623\u0643\u0628\u0631 \u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u062a\u0643\u0648\u064a\u0646\u0627\u062a \u0627\u0644\u0645\u0645\u0643\u0646\u0629. \u064a\u064f\u0631\u0645\u0632 \u0625\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0642\u0635\u0649 \u0628\u0640 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{max}<\/span><\/span>. \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0642\u062f\u064a\u0631 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645\u0629 \u0628\u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:\n<\/p>\n<ul>\n<ol>\n\t\t<strong>\u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0639\u0627\u062f\u064a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{max} = 10^{\\log(e)\\left[15\\cdot10^6 - \\ln\\left(15\\pi\\cdot10^6 \/ 2 \\right) \\right]\/2} \\approx 10^{6.514.413,542}<\/span><\/span>\n\t<\/ol>\n<ol>\n\t\t<strong>\u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0645\u0628\u0633\u0637:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{max} = 10^{\\log(e)\\left[15\\cdot10^6 \\right]\/2} \\approx 10^{6.514.417,229}<\/span><\/span>\n\t<\/ol>\n<\/ul>\n<p>\n\t\u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u062a\u0642\u062f\u064a\u0631\u064a\u0646 \u062d\u0648\u0627\u0644\u064a 4 \u0645\u0631\u0627\u062a\u0628 \u0645\u0646 \u062d\u064a\u062b \u0627\u0644\u062d\u062c\u0645 (\u0648\u0647\u0648 \u0645\u0627 \u0642\u062f \u064a\u0628\u062f\u0648 \u0643\u0628\u064a\u0631\u064b\u0627)\u060c \u0625\u0644\u0627 \u0623\u0646 \u0647\u0630\u0627 \u0644\u064a\u0633 \u0645\u0647\u0645\u064b\u0627 \u0641\u0639\u0644\u064a\u064b\u0627 \u0628\u062c\u0627\u0646\u0628 \u0623\u0643\u062b\u0631 \u0645\u0646 6 \u0645\u0644\u0627\u064a\u064a\u0646 \u0648\u0646\u0635\u0641 \u0645\u0631\u062a\u0628\u0629 \u0645\u0646 \u062d\u064a\u062b \u0627\u0644\u062d\u062c\u0645.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0643\u0645 \u0639\u062f\u062f \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0644\u062a\u0631\u062a\u064a\u0628 \u0646\u0638\u0627\u0645 \u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0645\u0643\u0648\u0646 \u0645\u0646 \u0645\u0644\u0627\u064a\u064a\u0646 \u0627\u0644\u0639\u0646\u0627\u0635\u0631\u061f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u0646\u0627\u0642\u0634 \u0643\u064a\u0641 \u062a\u064f\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0645\u0646 \u0627\u0644\u0625\u062c\u0627\u0628\u0629 \u0639\u0644\u0649 \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0641\u064a \u0633\u064a\u0627\u0642 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\u060c \u0628\u062f\u0621\u064b\u0627 \u0645\u0646 \u062a\u0648\u0632\u064a\u0639 \u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0637\u0627\u0642\u0629 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0630\u0631\u064a\u0629 \u0648\u062d\u062a\u0649 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0643\u0648\u064a\u0646\u0627\u062a \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0630\u0627\u062a \u0627\u0644\u0646\u0637\u0627\u0642 \u0627\u0644\u0643\u0628\u064a\u0631. \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0623\u062f\u0648\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629\u060c \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30534,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":3,"footnotes":""},"categories":[925,641],"tags":[],"class_list":["post-31198","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-925","category-641"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/ar\/\u0645\u0634\u0627\u0643\u0644-\u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629-\u0641\u064a-\u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627-\u0627\u0644\u062d\u0631\u0627\u0631\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\" \/>\n<meta property=\"og:description\" content=\"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/ar\/\u0645\u0634\u0627\u0643\u0644-\u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629-\u0641\u064a-\u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627-\u0627\u0644\u062d\u0631\u0627\u0631\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-28T13:00:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-01-12T13:22:07+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\" \/>\n<meta name=\"twitter:description\" content=\"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\",\"datePublished\":\"2021-03-28T13:00:14+00:00\",\"dateModified\":\"2025-01-12T13:22:07+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/\"},\"wordCount\":668,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg\",\"articleSection\":[\"\u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\",\"\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/\",\"url\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/\",\"name\":\"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg\",\"datePublished\":\"2021-03-28T13:00:14+00:00\",\"dateModified\":\"2025-01-12T13:22:07+00:00\",\"description\":\"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.\",\"breadcrumb\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg\",\"width\":1792,\"height\":1024,\"caption\":\"Combinatoria en termodin\u00e1mica, Combinatorics in thermodynamics, Combinat\u00f3ria em termodin\u00e2mica, \u70ed\u529b\u5b66\u4e2d\u7684\u7ec4\u5408\u5b66, \u0627\u0644\u062a\u0631\u0643\u064a\u0628\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629, \u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0938\u0902\u092f\u094b\u091c\u0928, \u041a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0430 \u0432 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0435, \u0627\u0644\u062a\u0631\u0643\u064a\u0628\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\/\/toposuranos.com\/material\/#website\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"name\":\"toposuranos.com\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\/\/toposuranos.com\/material\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\",\"name\":\"toposuranos.com\/material\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\/material\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/groups\/toposuranos\",\"https:\/\/x.com\/topuranos\",\"https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\/\/www.linkedin.com\/company\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\/\/toposuranos.com\/material\"],\"url\":\"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 - toposuranos.com\/material","description":"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/ar\/\u0645\u0634\u0627\u0643\u0644-\u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629-\u0641\u064a-\u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627-\u0627\u0644\u062d\u0631\u0627\u0631\/","og_locale":"es_ES","og_type":"article","og_title":"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629","og_description":"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.","og_url":"http:\/\/toposuranos.com\/material\/ar\/\u0645\u0634\u0627\u0643\u0644-\u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629-\u0641\u064a-\u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627-\u0627\u0644\u062d\u0631\u0627\u0631\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-03-28T13:00:14+00:00","article_modified_time":"2025-01-12T13:22:07+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA-1024x585.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629","twitter_description":"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629","datePublished":"2021-03-28T13:00:14+00:00","dateModified":"2025-01-12T13:22:07+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/"},"wordCount":668,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg","articleSection":["\u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629","\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/","url":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/","name":"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg","datePublished":"2021-03-28T13:00:14+00:00","dateModified":"2025-01-12T13:22:07+00:00","description":"\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0633\u0646\u0631\u0627\u062c\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0648\u0635\u064a\u063a\u0629 \u0633\u062a\u064a\u0631\u0644\u064a\u0646\u063a \u0641\u064a \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629 \u0645\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629.","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/12\/PROBLEMASDECOMBINATORIA.jpg","width":1792,"height":1024,"caption":"Combinatoria en termodin\u00e1mica, Combinatorics in thermodynamics, Combinat\u00f3ria em termodin\u00e2mica, \u70ed\u529b\u5b66\u4e2d\u7684\u7ec4\u5408\u5b66, \u0627\u0644\u062a\u0631\u0643\u064a\u0628\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629, \u0925\u0930\u094d\u092e\u094b\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 \u0938\u0902\u092f\u094b\u091c\u0928, \u041a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0430 \u0432 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0435, \u0627\u0644\u062a\u0631\u0643\u064a\u0628\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629"},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%a7%d9%83%d9%84-%d8%a7%d9%84%d8%aa%d9%88%d8%a7%d9%81%d9%82%d9%8a%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d8%af%d9%8a%d9%86%d8%a7%d9%85%d9%8a%d9%83%d8%a7-%d8%a7%d9%84%d8%ad%d8%b1%d8%a7%d8%b1\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u0627 \u0627\u0644\u062d\u0631\u0627\u0631\u064a\u0629"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/31198","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=31198"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/31198\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/30534"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=31198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=31198"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=31198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}