{"id":31205,"date":"2021-03-28T13:00:38","date_gmt":"2021-03-28T13:00:38","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=31205"},"modified":"2025-01-12T13:33:34","modified_gmt":"2025-01-12T13:33:34","slug":"%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%ba%d0%be%d0%bc%d0%b1%d0%b8%d0%bd%d0%b0%d1%82%d0%be%d1%80%d0%b8%d0%ba%d0%b8-%d0%b2-%d1%82%d0%b5%d1%80%d0%bc%d0%be%d0%b4%d0%b8%d0%bd%d0%b0%d0%bc","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%be%d0%b1%d0%bb%d0%b5%d0%bc%d1%8b-%d0%ba%d0%be%d0%bc%d0%b1%d0%b8%d0%bd%d0%b0%d1%82%d0%be%d1%80%d0%b8%d0%ba%d0%b8-%d0%b2-%d1%82%d0%b5%d1%80%d0%bc%d0%be%d0%b4%d0%b8%d0%bd%d0%b0%d0%bc\/","title":{"rendered":"\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438 \u0432 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0435"},"content":{"rendered":"<style>\n<p>\tp, ul, ol {\n\t\ttext-align: justify;\n\t}<\/p>\n<p>\th1, h2 {\n\t\ttext-align: center;\n\t}<\/p>\n<\/style>\n<h1>\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438 \u0432 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0435<\/h1>\n<p style=\"text-align:center;\"><em>\u0421\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0434\u043b\u044f \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0435\u0439 \u0438\u0437 \u043c\u0438\u043b\u043b\u0438\u043e\u043d\u043e\u0432 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432? \u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b 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\u043a\u0430\u0436\u0443\u0442\u0441\u044f \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u043c\u0438.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0423\u0447\u0435\u0431\u043d\u044b\u0435 \u0446\u0435\u043b\u0438:<\/strong><br \/>\n\u041f\u043e \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0441\u043c\u043e\u0436\u0435\u0442:<\/p>\n<ol>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong>, \u043a\u0430\u043a \u0437\u0430\u0434\u0430\u0447\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u044e\u0442\u0441\u044f \u0432 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0435 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0438, \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e \u0432 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c.<\/li>\n<li><strong>\u0420\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c<\/strong> \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0430\u0442\u043e\u043c\u043d\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c<\/strong> \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0421\u0442\u0438\u0440\u043b\u0438\u043d\u0433\u0430 \u0434\u043b\u044f \u043e\u0446\u0435\u043d\u043a\u0438 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><u>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415:<\/u><br \/>\n<a href=\"#1\"><strong>\u0417\u0430\u0434\u0430\u0447\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u0417\u0430\u0434\u0430\u0447\u0438 \u0441 \u0431\u043e\u043b\u044c\u0448\u0438\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438<\/strong><\/a><br \/>\n<a href=\"#3\">\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0421\u0442\u0438\u0440\u043b\u0438\u043d\u0433\u0430 \u0434\u043b\u044f \u043e\u0446\u0435\u043d\u043a\u0438 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b<\/a><br \/>\n<a href=\"#4\"><em>\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0447\u0435\u0440\u0435\u0437 \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435<\/em><\/a><br \/>\n<a href=\"#5\"><em>\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0447\u0435\u0440\u0435\u0437 \u043e\u0431\u044b\u0447\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435<\/em><\/a><br \/>\n<a href=\"#6\"><strong>\u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0445 \u0440\u0430\u0441\u0447\u0435\u0442\u043e\u0432 \u0438 \u043e\u0446\u0435\u043d\u043a\u0438 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b<\/strong><\/a><br \/>\n<a href=\"#7\">\u041f\u0440\u0438\u043c\u0435\u0440 1: \u0411\u043e\u043b\u044c\u0448\u0438\u0435 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0430\u043b\u044b<\/a><br \/>\n<a href=\"#8\">\u041f\u0440\u0438\u043c\u0435\u0440 2: \u0411\u043e\u043b\u044c\u0448\u0438\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438<\/a>\n<\/p>\n<p>\u041e\u0434\u0438\u043d \u0438\u0437 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u0445 \u0432\u043e\u043f\u0440\u043e\u0441\u043e\u0432 \u0432 \u0444\u0438\u0437\u0438\u043a\u0435: \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u043c\u043e\u0436\u043d\u043e \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u0430\u043d\u043d\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443? \u0422\u0430\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438 \u0447\u0430\u0441\u0442\u043e \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f 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\u0410\u0432\u043e\u0433\u0430\u0434\u0440\u043e<\/a><\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">N_A<\/span>, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u043b\u043e\u0436\u043d\u043e \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u0441 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430\u043c\u0438 \u0442\u0430\u043a\u043e\u0433\u043e \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0430.<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0417\u0430\u0434\u0430\u0447\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/K7_De9wux4A?si=q93_T8xh15EdfJ6B\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043d\u044f\u0442\u044c \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0437\u0430\u0434\u0430\u0447, \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u0445 \u0441 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u043e\u0439 \u0432 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0435, \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<h4>\u041f\u0440\u0438\u043c\u0435\u0440: \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0434\u043b\u044f \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u044d\u043d\u0435\u0440\u0433\u0438\u0438<\/h4>\n<p>\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 10 \u0430\u0442\u043e\u043c\u043e\u0432. \u041a\u0430\u0436\u0434\u044b\u0439 \u0430\u0442\u043e\u043c \u043c\u043e\u0436\u0435\u0442 \u0445\u0440\u0430\u043d\u0438\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e 1 \u0438\u043b\u0438 0 \u0435\u0434\u0438\u043d\u0438\u0446 \u044d\u043d\u0435\u0440\u0433\u0438\u0438, \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u044b\u0445 <strong>\u043a\u0432\u0430\u043d\u0442\u0430\u043c\u0438 \u044d\u043d\u0435\u0440\u0433\u0438\u0438<\/strong>. \u0421\u043a\u043e\u043b\u044c\u043a\u0438\u043c\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u044d\u0442\u0438 \u043a\u0432\u0430\u043d\u0442\u044b, \u0435\u0441\u043b\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c (a) 10 \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u044d\u043d\u0435\u0440\u0433\u0438\u0438 \u0438 (b) 5 \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u044d\u043d\u0435\u0440\u0433\u0438\u0438?<\/p>\n<h5>\u0420\u0435\u0448\u0435\u043d\u0438\u0435<\/h5>\n<p>\u041c\u044b \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0430\u0442\u043e\u043c\u044b \u043a\u0430\u043a \u044f\u0447\u0435\u0439\u043a\u0438, \u0434\u043e\u0441\u0442\u0443\u043f\u043d\u044b\u0435 \u0434\u043b\u044f \u0445\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u044d\u043d\u0435\u0440\u0433\u0438\u0438. \u0415\u0441\u043b\u0438 \u044f\u0447\u0435\u0439\u043a\u0430 \u0437\u0430\u043f\u043e\u043b\u043d\u0435\u043d\u0430, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0439 \u0430\u0442\u043e\u043c \u0443\u0436\u0435 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0441\u0432\u043e\u0439 \u043a\u0432\u0430\u043d\u0442 \u044d\u043d\u0435\u0440\u0433\u0438\u0438.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-zJa7H7iMOGY\/YF3QhG94SoI\/AAAAAAAAEuI\/olfdSHfeJOgKea3vHXEAyr5QCJ1ZjmcpgCLcBGAsYHQ\/s839\/cuantodeenergia.PNG\" \n               class=\"aligncenter lazyload\" alt=\"\u0417\u0430\u0434\u0430\u0447\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438 \u0432 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0435\" width=\"400\" height=\"200\" \/><\/center><\/p>\n<p>\u0414\u043b\u044f \u043f\u043e\u0434\u0441\u0447\u0435\u0442\u0430 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u044d\u043d\u0435\u0440\u0433\u0438\u0438 \u043c\u0435\u0436\u0434\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u044f\u0447\u0435\u0439\u043a\u0430\u043c\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\binom{n}{k}=\\dfrac{n!}{k!(n-k)!}<\/span><\/span><\/p>\n<p>\u042d\u0442\u043e\u0442 \u0440\u0430\u0441\u0447\u0435\u0442 \u0434\u0430\u0435\u0442 \u043d\u0430\u043c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0439 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span>.<\/p>\n<p><strong>(a)<\/strong> \u0415\u0441\u043b\u0438 10 \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u044b \u043c\u0435\u0436\u0434\u0443 10 \u044f\u0447\u0435\u0439\u043a\u0430\u043c\u0438, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u0438\u043d \u0441\u043f\u043e\u0441\u043e\u0431 \u044d\u0442\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega=1<\/span><\/span>:<\/p>\n<p style=\"text-align:center;\"><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><\/p>\n<p><strong>(b)<\/strong> \u0414\u043b\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f 5 \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u043c\u0435\u0436\u0434\u0443 10 \u044f\u0447\u0435\u0439\u043a\u0430\u043c\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\Omega &amp;= \\displaystyle\\binom{10}{5} \\\\ \\\\\n\n&amp;=\\dfrac{10!}{5!(10-5)!} = \\dfrac{10!}{5!\\cdot 5!} \\\\ \\\\\n\n&amp;= \\dfrac{5! \\cdot 6\\cdot 7\\cdot 8 \\cdot 9\\cdot 10}{5! \\cdot 2\\cdot 3\\cdot 4\\cdot 5} \\\\ \\\\\n\n&amp;= \\dfrac{ 7\\cdot 8 \\cdot 9\\cdot 10}{ 4\\cdot 5} = 7\\cdot 2 \\cdot 9 \\cdot 2 = 252\n\n\\end{array}<\/span>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 252 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0417\u0430\u0434\u0430\u0447\u0438 \u0441 \u0431\u043e\u043b\u044c\u0448\u0438\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438<\/h2>\n<p>\u0422\u043e, \u0447\u0442\u043e \u043c\u044b \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u0434\u043e \u0441\u0438\u0445 \u043f\u043e\u0440, \u2014 \u044d\u0442\u043e \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u0430\u0447\u0430\u043b\u043e. \u0415\u0441\u043b\u0438 \u043c\u044b \u0440\u0430\u0441\u0448\u0438\u0440\u0438\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0438\u0437 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 (b) \u0434\u043e 100 \u0430\u0442\u043e\u043c\u043e\u0432 \u0438 50 \u043a\u0432\u0430\u043d\u0442\u043e\u0432, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega \\approx 10^{28}<\/span><\/span>. \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044c\u0442\u0435, \u0447\u0442\u043e \u0442\u043e\u0442 \u0436\u0435 \u0440\u0430\u0441\u0447\u0435\u0442 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043e\u0434\u043d\u043e\u0433\u043e \u043c\u043e\u043b\u044f \u0430\u0442\u043e\u043c\u043e\u0432; \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0431\u0443\u0434\u0435\u0442 \u043d\u0435\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u044b\u043c.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0421\u0442\u0438\u0440\u043b\u0438\u043d\u0433\u0430 \u0434\u043b\u044f \u043e\u0446\u0435\u043d\u043a\u0438 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b<\/h3>\n<p>\u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega = \\binom{n}{k}<\/span><\/span> \u0434\u043b\u044f \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>, \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e \u043a\u043e\u0433\u0434\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span><\/span>, \u0447\u0442\u043e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0441\u043b\u0443\u0447\u0430\u044e, \u043a\u043e\u0433\u0434\u0430 \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u044e\u0442\u0441\u044f \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043f\u043e\u043b\u0435\u0437\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0421\u0442\u0438\u0440\u043b\u0438\u043d\u0433\u0430.<\/p>\n<p>\u0427\u0442\u043e\u0431\u044b \u0441\u043f\u0440\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u0441 \u0447\u0438\u0441\u043b\u0430\u043c\u0438 \u0442\u0430\u043a\u043e\u0433\u043e \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0430, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u044c \u0440\u0430\u0441\u0447\u0435\u0442, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u044b:<\/p>\n<p style=\"text-align:center;\"><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><\/p>\n<p>\u042d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u043d\u043e \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0421\u0442\u0438\u0440\u043b\u0438\u043d\u0433\u0430 \u0434\u043b\u044f \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0430\u043b\u0430. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0435\u0441\u0442\u044c \u0434\u0432\u0430 \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0430: \u043e\u0431\u044b\u0447\u043d\u043e\u0435 \u0438 \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435:<\/p>\n<ul>\n<li><strong>\u041e\u0431\u044b\u0447\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435:<\/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><\/li>\n<li><strong>\u0423\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(n!) \\approx n\\ln(n) - n<\/span><\/span><\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/p>\n<h4>\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0447\u0435\u0440\u0435\u0437 \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435<\/h4>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/fnt99FeeHPM?si=H6r-5GhO2yqaeaXd\" title=\"YouTube \u0432\u0438\u0434\u0435\u043e \u043f\u043b\u0435\u0435\u0440\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\ln(\\Omega) &amp; \\approx n\\ln(n) - n - (n-k)\\ln(n-k) + (n-k) - k\\ln(k) + k \\\\ \\\\\n\n&amp;= n\\ln(n) - (n-k)\\ln(n-k) - k\\ln(k) \\\\ \\\\\n\n&amp;= n\\ln(n) - n\\ln(n-k) + k\\ln(n-k) - k\\ln(k) \\\\ \\\\\n\n&amp;= \\ln\\left[ \\left( \\dfrac{n}{n-k} \\right)^n \\right] + k\\ln\\left( \\dfrac{n-k}{k} \\right) \\\\ \\\\\n\n&amp;= \\ln\\left[ \\dfrac{1}{\\left(1 - \\dfrac{k}{n} \\right)^n} \\right] + k\\ln\\left( \\dfrac{n}{k} - 1 \\right)\n\n\\end{array}<\/span>\n<p>\u0414\u043b\u044f \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0432\u044f\u0437\u044c:<\/p>\n<p style=\"text-align:center;\"><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><\/p>\n<p>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e:<\/p>\n<p style=\"text-align:center;\"><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><\/p>\n<p>\u0412 \u0438\u0442\u043e\u0433\u0435, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434 \u043a \u0434\u0435\u0441\u044f\u0442\u0438\u0447\u043d\u044b\u043c \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430\u043c, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p style=\"text-align:center;\"><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><\/p>\n<p>\u0418 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/p>\n<p style=\"text-align:center;\"><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><\/p>\n<p>\u0425\u043e\u0442\u044f \u044d\u0442\u043e\u0442 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043d\u0435 \u0434\u0430\u0435\u0442 \u0442\u043e\u0447\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span>, \u043e\u043d \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0446\u0438\u0444\u0440, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0445 \u0434\u043b\u044f \u0435\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f, \u0438 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0442\u043e\u0447\u043d\u0435\u0435 \u0441 \u0443\u0432\u0435\u043b\u0438\u0447\u0435\u043d\u0438\u0435\u043c <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>. \u0421 \u044d\u0442\u0438\u043c \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0447\u0442\u043e \u0434\u043e\u0441\u0442\u0443\u043f\u043d\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u043d\u0441\u0442\u0432\u0443 \u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440\u043e\u0432.<\/p>\n<p>\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u044d\u0442\u043e\u0442 \u043f\u043e\u0434\u0445\u043e\u0434 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0431\u044b\u0441\u0442\u0440\u043e \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> \u0434\u043b\u044f \u0431\u043e\u043b\u044c\u0448\u043e\u0433\u043e <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span>. \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span>, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Max}\\left(\\Omega\\right) \\approx 10^{\\dfrac{n}{2}\\log(e)\\left[1 + \\ln\\left( \\dfrac{n}{n\/2} - 1 \\right) \\right]} = 10^{ n\\log(e)\/2 } <\/span><\/span><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h4>\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0447\u0435\u0440\u0435\u0437 \u043e\u0431\u044b\u0447\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435<\/h4>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/i3OO4lHV24Q?si=jEPCafXqgVxNYqH-\" title=\"YouTube \u0432\u0438\u0434\u0435\u043e \u043f\u043b\u0435\u0435\u0440\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u0425\u043e\u0442\u044f \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0447\u0435\u0440\u0435\u0437 \u043e\u0431\u044b\u0447\u043d\u043e\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435 \u0434\u0430\u0435\u0442 \u0431\u043e\u043b\u0435\u0435 \u0442\u043e\u0447\u043d\u044b\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u043e\u043d\u043e \u0432\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0434\u043b\u044f \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u043f\u0440\u0438\u0432\u043e\u0434\u044f\u0442 \u043a \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c, \u0441\u0445\u043e\u0436\u0438\u043c \u0441 \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u044b\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435\u043c. \u042d\u0442\u043e\u0442 \u043c\u0435\u0442\u043e\u0434 \u043f\u043e\u0432\u0442\u043e\u0440\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u043c\u043d\u043e\u0433\u0438\u0435 \u0440\u0430\u0441\u0447\u0435\u0442\u044b, \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043d\u044b\u0435 \u0440\u0430\u043d\u0435\u0435 \u0434\u043b\u044f \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u044f, \u0438 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\ln(\\Omega) &amp; = &amp; \\ln\\left(\\dfrac{n!}{k!(n-k)!}\\right)= \\ln(n!) - \\ln((n-k)!) - \\ln(k!) \\\\ \\\\\n\n&amp; \\approx &amp; \\color{red}\\dfrac{1}{2}\\ln(2n\\pi)\\color{black} + n\\ln(n) - n \\\\ \\\\\n\n&amp; &amp; \\color{red}-\\dfrac{1}{2}\\ln(2(n-k)\\pi)\\color{black} - (n-k)\\ln(n-k) + (n-k) \\\\ \\\\\n\n&amp; &amp; \\color{red}-\\dfrac{1}{2}\\ln(2k\\pi)\\color{black} - k\\ln(k) + k\n\n\\end{array}<\/span>\n<p>\u0427\u0430\u0441\u0442\u0438, \u0432\u044b\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0435 \u043a\u0440\u0430\u0441\u043d\u044b\u043c, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0441\u043e\u0431\u043e\u0439 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u0432 \u043e\u0431\u044b\u0447\u043d\u043e\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438. \u041e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0441 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c\u0438 \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u044f. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\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&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\\end{array}<\/span>\n<p>\u0417\u0430\u0442\u0435\u043c, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u0434 \u043a \u0434\u0435\u0441\u044f\u0442\u0438\u0447\u043d\u044b\u043c \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430\u043c, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p style=\"text-align:center;\"><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><\/p>\n<p>\u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u0440\u0438 \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0435 \u043a \u0434\u0435\u0441\u044f\u0442\u0438\u0447\u043d\u043e\u0439 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0442\u0435:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\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]}\n\n<\/span>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c, \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c\u0443, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u044d\u0442\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b, \u0432\u0437\u044f\u0432 <span class=\"katex-eq\" data-katex-display=\"false\">k=n\/2<\/span>. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0431\u0443\u0434\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\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&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\\end{array}<\/span>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0445 \u0440\u0430\u0441\u0447\u0435\u0442\u043e\u0432 \u0438 \u043e\u0446\u0435\u043d\u043a\u0438 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/M7NrtICrSzU?si=6UT34333Wp5YwFU1\" title=\"YouTube \u0432\u0438\u0434\u0435\u043e \u043f\u043b\u0435\u0435\u0440\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u041f\u0440\u0438\u043c\u0435\u0440 1: \u0411\u043e\u043b\u044c\u0448\u0438\u0435 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0430\u043b\u044b<\/h3>\n<p>\u041e\u0446\u0435\u043d\u0438\u043c \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(10^{50}\\right)!<\/span><\/span>, \u0442\u043e \u0435\u0441\u0442\u044c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0446\u0438\u0444\u0440, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0445 \u0434\u043b\u044f \u0437\u0430\u043f\u0438\u0441\u0438 \u044d\u0442\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430.<\/p>\n<h5>\u0420\u0435\u0448\u0435\u043d\u0438\u0435<\/h5>\n<p>\u0414\u043b\u044f \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0421\u0442\u0438\u0440\u043b\u0438\u043d\u0433\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\ln\\left[ \\left(10^{50}\\right)! \\right] &amp;\\approx 10^{50}\\ln\\left(10^{50}\\right) - 10^{50}\\\\ \\\\\n\n&amp;= \\left[\\ln\\left(10^{50}\\right) -1\\right]10^{50}  \\\\ \\\\\n\n&amp;= \\left[50\\ln(10)-1 \\right]10^{50} \\\\ \\\\\n\n\\end{array}\n\n<\/span>\n<p>\u0414\u0430\u043b\u0435\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u043c \u043f\u0435\u0440\u0435\u0445\u043e\u0434 \u043a \u0434\u0435\u0441\u044f\u0442\u0438\u0447\u043d\u044b\u043c \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430\u043c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\ln\\left[ \\left(10^{50}\\right)! \\right] = \\dfrac{\\log\\left[\\left(10^{50}\\right)!\\right]}{\\log{e}}\n\n<\/span>\n<p>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\log\\left[ \\left(10^{50}\\right)! \\right] \\approx \\log(e)\\left[50\\ln(10)-1 \\right]10^{50}\n\n<\/span>\n<p>\u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u044f \u043a \u0434\u0435\u0441\u044f\u0442\u0438\u0447\u043d\u043e\u0439 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0442\u0435, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\left(10^{50}\\right)!  \\approx  10^{\\log(e)\\left[50\\ln(10)-1 \\right]10^{50}} = 10^{49,5657 \\cdot 10^{50}}\n\n<\/span>\n<p>\u041f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 10 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b, \u0434\u0430\u0432\u0430\u044f \u043e\u0446\u0435\u043d\u043a\u0443 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0430 \u0446\u0438\u0444\u0440 \u0432 \u0447\u0438\u0441\u043b\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(10^{50}\\right)!<\/span><\/span>.<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<h3>\u041f\u0440\u0438\u043c\u0435\u0440 2: \u0411\u043e\u043b\u044c\u0448\u0438\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438<\/h3>\n<p>\u0421\u0440\u0435\u0434\u043d\u0438\u0439 \u0434\u043e\u043c \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e 12 \u0432\u044b\u043a\u043b\u044e\u0447\u0430\u0442\u0435\u043b\u0435\u0439 \u0441\u0432\u0435\u0442\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0432\u043a\u043b\u044e\u0447\u0435\u043d\u044b \u0438\u043b\u0438 \u0432\u044b\u043a\u043b\u044e\u0447\u0435\u043d\u044b. \u0412 \u0441\u0440\u0435\u0434\u043d\u0435\u043c, \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0434\u043e\u043c\u0435 \u0436\u0438\u0432\u0443\u0442 4 \u0447\u0435\u043b\u043e\u0432\u0435\u043a\u0430. \u0415\u0441\u043b\u0438 \u0432 \u0433\u043e\u0440\u043e\u0434\u0435 \u043f\u0440\u043e\u0436\u0438\u0432\u0430\u0435\u0442 5 \u043c\u0438\u043b\u043b\u0438\u043e\u043d\u043e\u0432 \u0447\u0435\u043b\u043e\u0432\u0435\u043a, \u0442\u043e \u0441\u043a\u043e\u043b\u044c\u043a\u0438\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u043a\u043b\u044e\u0447\u0435\u043d\u0430 \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0430 \u0432\u044b\u043a\u043b\u044e\u0447\u0430\u0442\u0435\u043b\u0435\u0439 \u0433\u043e\u0440\u043e\u0434\u0430?<\/p>\n<h5>\u0420\u0435\u0448\u0435\u043d\u0438\u0435<\/h5>\n<p>\u041e\u0431\u0449\u0435\u0435 \u0447\u0438\u0441\u043b\u043e \u0432\u044b\u043a\u043b\u044e\u0447\u0430\u0442\u0435\u043b\u0435\u0439 \u0441\u0432\u0435\u0442\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0432 \u0433\u043e\u0440\u043e\u0434\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\nn &amp;=&amp;\\dfrac{\\text{\u0447\u0438\u0441\u043b\u043e \u0436\u0438\u0442\u0435\u043b\u0435\u0439 \u0433\u043e\u0440\u043e\u0434\u0430}}{\\text{\u043b\u044e\u0434\u0435\u0439 \u043d\u0430 \u0434\u043e\u043c}} \\times \\text{\u0432\u044b\u043a\u043b\u044e\u0447\u0430\u0442\u0435\u043b\u0435\u0439 \u043d\u0430 \u0434\u043e\u043c} \\\\ \\\\\n\n&amp;=&amp; \\dfrac{5\\cdot 10^6}{4}\\cdot 12 = 15\\cdot 10^6\n\n\\end{array}\n\n<\/span>\n<p>\u041c\u0430\u043a\u0440\u043e\u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0435, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0435\u0435 \u0438\u0437 \u0432\u0441\u0435\u0445 \u043c\u0438\u043a\u0440\u043e\u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0439, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0430 \u0432\u044b\u043a\u043b\u044e\u0447\u0430\u0442\u0435\u043b\u0435\u0439 \u0432\u043a\u043b\u044e\u0447\u0435\u043d\u0430, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043c\u0430\u043a\u0440\u043e\u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u0441 \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0438\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439. \u041e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044f \u044d\u0442\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u043a\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{max}<\/span><\/span>, \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043e\u0446\u0435\u043d\u043a\u0438 \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u043c\u0435\u0442\u043e\u0434\u0430:<\/p>\n<ul>\n<ol><strong>\u041e\u0431\u044b\u0447\u043d\u0430\u044f \u043e\u0446\u0435\u043d\u043a\u0430:<\/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><\/ol>\n<ol><strong>\u0423\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u0430\u044f \u043e\u0446\u0435\u043d\u043a\u0430:<\/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><\/ol>\n<\/ul>\n<p>\u0425\u043e\u0442\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043e\u0446\u0435\u043d\u043a\u0430\u043c\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0430\u0437\u043d\u0438\u0446\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u0432 4 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b (\u0447\u0442\u043e \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u044c\u0441\u044f \u0437\u043d\u0430\u0447\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c), \u043d\u0430 \u0444\u043e\u043d\u0435 \u0431\u043e\u043b\u0435\u0435 \u0447\u0435\u043c 6,5 \u043c\u0438\u043b\u043b\u0438\u043e\u043d\u043e\u0432 \u043f\u043e\u0440\u044f\u0434\u043a\u043e\u0432 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u044d\u0442\u043e \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043d\u0435\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0438 \u0432 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0435 \u0421\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0434\u043b\u044f \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u0438 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0435\u0439 \u0438\u0437 \u043c\u0438\u043b\u043b\u0438\u043e\u043d\u043e\u0432 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432? \u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442 \u043e\u0442\u0432\u0435\u0442\u0438\u0442\u044c \u043d\u0430 \u044d\u0442\u043e\u0442 \u0432\u043e\u043f\u0440\u043e\u0441 \u0432 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0435 \u0442\u0435\u0440\u043c\u043e\u0434\u0438\u043d\u0430\u043c\u0438\u043a\u0438 \u2014 \u043e\u0442 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043a\u0432\u0430\u043d\u0442\u043e\u0432 \u044d\u043d\u0435\u0440\u0433\u0438\u0438 \u0432 \u0430\u0442\u043e\u043c\u043d\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0445 \u0434\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0439 \u0432 \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u043d\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0445. \u0421 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0442\u0430\u043a\u0438\u0445 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u043e\u0432, \u043a\u0430\u043a \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u0438\u043a\u0430, \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u044b \u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0421\u0442\u0438\u0440\u043b\u0438\u043d\u0433\u0430, 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