{"id":26482,"date":"2021-03-26T13:00:30","date_gmt":"2021-03-26T13:00:30","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26482"},"modified":"2024-05-21T09:44:00","modified_gmt":"2024-05-21T09:44:00","slug":"%e8%ae%a1%e6%95%b0%e6%8a%80%e6%9c%af%ef%bc%9a%e6%8e%92%e5%88%97%e3%80%81%e5%8f%98%e6%8d%a2%e5%92%8c%e7%bb%84%e5%90%88","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e8%ae%a1%e6%95%b0%e6%8a%80%e6%9c%af%ef%bc%9a%e6%8e%92%e5%88%97%e3%80%81%e5%8f%98%e6%8d%a2%e5%92%8c%e7%bb%84%e5%90%88\/","title":{"rendered":"\u8ba1\u6570\u6280\u672f\uff1a\u6392\u5217\u3001\u53d8\u6362\u548c\u7ec4\u5408"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u8ba1\u6570\u6280\u672f\uff1a\u6392\u5217\u3001\u53d8\u6362\u548c\u7ec4\u5408<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u5728\u6982\u7387\u7814\u7a76\u4e2d\uff0c\u8ba1\u6570\u6280\u672f\u662f\u6d4b\u91cf\u6837\u672c\u7a7a\u95f4\u548c\u5f85\u6d4b\u4e8b\u4ef6\u57fa\u6570\u7684\u57fa\u672c\u5de5\u5177\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7531\u4e8e\u5728\u7b49\u6982\u7387\u7ed3\u679c\u7684\u5b9e\u9a8c\u4e2d\u4f7f\u7528\u65b9\u4fbf\uff0c\u7ec4\u5408\u3001\u53d8\u6362\u548c\u6392\u5217\u6280\u672f\u662f\u6700\u5e38\u7528\u7684\u3002\u901a\u8fc7\u5c06\u6982\u7387\u6d4b\u91cf\u4e3a\u76f8\u5bf9\u9891\u7387\u7684\u6781\u9650\uff0c\u53ef\u4ee5\u5c06\u4e8b\u4ef6\u7684\u6982\u7387\u8868\u793a\u4e3a\u57fa\u6570\u7684\u5546\u3002\u56e0\u6b64\uff0c\u6982\u7387\u8ba1\u7b97\u5f52\u7ed3\u4e3a\u8ba1\u7b97\u6837\u672c\u7a7a\u95f4\u548c\u5f85\u6d4b\u4e8b\u4ef6\u7684\u57fa\u6570\u3002\u5728\u8fd9\u65b9\u9762\uff0c\u901a\u8fc7\u7b49\u6982\u7387\u7ed3\u679c\u5b9e\u9a8c\u83b7\u5f97\u7684\u8ba1\u6570\u6280\u672f\u5bf9\u4e8e\u6982\u7387\u7814\u7a76\u81f3\u5173\u91cd\u8981\u3002\u901a\u8fc7\u5b9a\u4e49\u53d8\u6362\u3001\u7ec4\u5408\u548c\u6392\u5217\uff0c\u53ef\u4ee5\u6709\u6548\u4e14\u7cbe\u786e\u5730\u6d4b\u91cf\u96c6\u5408\u7684\u5927\u5c0f\u3002\u672c\u8bfe\u5c06\u4ecb\u7ecd\u4e00\u4e9b\u5177\u6709\u7b49\u6982\u7387\u7ed3\u679c\u7684\u5b9e\u9a8c\uff0c\u5e76\u5206\u6790\u5176\u6837\u672c\u7a7a\u95f4\u4ee5\u5f15\u5165\u8ba1\u6570\u6280\u672f\u3002\u4f7f\u7528\u8fd9\u4e9b\u5de5\u5177\uff0c\u53ef\u4ee5\u6d4b\u91cf\u5404\u79cd\u96c6\u5408\u7684\u5927\u5c0f\u5e76\u8ba1\u7b97\u7b49\u6982\u7387\u7ed3\u679c\u5b9e\u9a8c\u4e2d\u7684\u4e8b\u4ef6\u6982\u7387\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<strong>\u8bb0\u4f4f<\/strong>\u7528\u6709\u5229\u4e8b\u4ef6\u4e0e\u53ef\u80fd\u4e8b\u4ef6\u7684\u516c\u5f0f\u6765\u8ba1\u7b97\u4e8b\u4ef6\u7684\u6982\u7387\u3002<br \/>\n<strong>\u7406\u89e3<\/strong>\u6392\u5217\u3001\u53d8\u6362\u548c\u7ec4\u5408\u7684\u6982\u5ff5\u53ca\u5176\u5728\u6982\u7387\u8ba1\u7b97\u4e2d\u7684\u5e94\u7528\u3002<br \/>\n<strong>\u5206\u6790<\/strong>\u5e76\u89e3\u91ca\u6837\u672c\u7a7a\u95f4\u5927\u5c0f\u4e0e\u7b49\u6982\u7387\u7ed3\u679c\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6\u6982\u7387\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<br \/>\n<strong>\u8bc6\u522b<\/strong>\u53ef\u4ee5\u5728\u65e5\u5e38\u751f\u6d3b\u4e2d\u5e94\u7528\u7ec4\u5408\u3001\u53d8\u6362\u548c\u6392\u5217\u8ba1\u6570\u6280\u672f\u7684\u60c5\u51b5\uff0c\u4f8b\u5982\u5728\u8d4c\u535a\u6e38\u620f\u548c\u7ec4\u7ec7\u95ee\u9898\u4e2d\u3002\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u5185\u5bb9\u7d22\u5f15<\/strong><br \/>\n<a href=\"#1\"><strong>\u8ba1\u6570\u6280\u672f\u4e0e\u6982\u7387<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u8ba1\u6570\u6280\u672f\u7684\u83b7\u53d6<\/strong><\/a><br \/>\n<a href=\"#3\">\u5b9e\u9a8c1\uff08AORM\uff09\uff1a\u6267\u884c\u2014\u2014\u6309\u987a\u5e8f\u8bb0\u5f55\u2014\u2014\u91cd\u7f6e\uff0c\u91cd\u590dM\u6b21<\/a><br \/>\n<a href=\"#4\">\u5b9e\u9a8c2\uff08AOK\uff09\uff1a\u6267\u884c\u2014\u2014\u6309\u987a\u5e8f\u8bb0\u5f55\uff0c\u91cd\u590dK\u6b21<\/a><br \/>\n<a href=\"#5\">\u5b9e\u9a8c3\uff08ADK\uff09\uff1a\u6267\u884c\u2014\u2014\u65e0\u5e8f\u8bb0\u5f55\uff0c\u91cd\u590dK\u6b21<\/a><\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/72LBcZP7Fv4\" title=\"YouTube\u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u8ba1\u6570\u6280\u672f\u4e0e\u6982\u7387<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=7s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u7ec4\u5408\u3001\u53d8\u6362\u548c\u6392\u5217\u662f\u6982\u7387\u7814\u7a76\u4e2d\u6700\u5e38\u7528\u7684\u8ba1\u6570\u6280\u672f<\/span><\/strong><\/a>\uff0c\u56e0\u4e3a\u5b83\u4eec\u5728\u7b49\u6982\u7387\u7ed3\u679c\u7684\u5b9e\u9a8c\u4e2d\u63d0\u4f9b\u4e86\u5f88\u5927\u7684\u65b9\u4fbf\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u4e2d\u6700\u5177\u4ee3\u8868\u6027\u7684\u4f8b\u5b50\u6765\u81ea\u8d4c\u535a\u6e38\u620f\u3002\u5b83\u4eec\u901a\u5e38\u6d89\u53ca\u4e00\u4e2a\u6837\u672c\u7a7a\u95f4 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega = \\{\\omega_1, \\omega_2, \\cdots, \\omega_N\\}<\/span> \u4e0a\u7684\u975e\u786e\u5b9a\u6027\u8fc7\u7a0b\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u6709\u4e00\u4e2a\u5171\u540c\u7684\u7279\u70b9\uff0c\u5373\u5f62\u5f0f\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\{\\omega_i\\}\\in\\mathcal{A}_\\Omega<\/span> \u7684\u6240\u6709\u4e8b\u4ef6\uff0c\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">i\\in\\{1,2,\\cdots, n\\}<\/span>\uff0c\u5177\u6709\u76f8\u540c\u7684\u53d1\u751f\u6982\u7387\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u57fa\u4e8e <strong><a href=\"https:\/\/toposuranos.com\/el-espacio-de-probabilidades-medida-de-probabilidad\/\" target=\"_blank\" rel=\"noopener\">\u76f8\u5bf9\u9891\u7387\u6781\u9650\u7684\u6982\u7387\u6d4b\u91cf<\/a><\/strong>\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e8b\u4ef6\u7684\u6982\u7387\u5efa\u7acb\u4e3a\u57fa\u6570\u7684\u5546\u3002\u6b63\u5982\u6211\u4eec\u6240\u89c1\uff0c\u8fd9\u901a\u8fc7\u4ee5\u4e0b\u5173\u7cfb\u5b9e\u73b0\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(E) = \\displaystyle \\lim_{N\\to\\infty}g_N(E) = \\lim_{N\\to\\infty}\\frac{f_N(E)}{N}= \\frac{\\# E}{\\# \\Omega}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u91cc\u7b26\u53f7\u201c#\u201d\u8868\u793a\u96c6\u5408\u7684\u57fa\u6570\u3002\u8fd9\u5c31\u662f\u6240\u8c13\u7684<strong>\u6709\u5229\u4e8b\u4ef6\u4e0e\u53ef\u80fd\u4e8b\u4ef6\u7684\u516c\u5f0f\u3002<\/strong><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u6982\u7387\u8ba1\u7b97\u5f52\u7ed3\u4e3a\u8ba1\u7b97\u6837\u672c\u7a7a\u95f4\u548c\u5f85\u6d4b\u4e8b\u4ef6\u7684\u57fa\u6570\u3002\u56e0\u6b64\uff0c\u9996\u5148\u590d\u4e60\u4e00\u4e9b<strong>\u8ba1\u6570\u6280\u672f<\/strong>\u5c06\u975e\u5e38\u6709\u7528\u3002<\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u8ba1\u6570\u6280\u672f\u7684\u83b7\u53d6<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=260s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>\u4e3a\u4e86\u5f15\u5165\u7ec4\u5408\u3001\u53d8\u6362\u548c\u6392\u5217<\/strong><\/span><\/a>\uff0c\u6211\u4eec\u5c06\u8bbe\u8ba1\u4e00\u4e9b\u5177\u6709\u7b49\u6982\u7387\u7ed3\u679c\u7684\u5b9e\u9a8c\uff0c\u5e76\u4ece\u4e2d\u8fdb\u884c\u63a8\u8bba\uff0c\u5f97\u51fa\u8fd9\u4e9b\u8ba1\u6570\u6280\u672f\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u53f0\u201c\u5b8c\u7f8e\u7684\u968f\u673a\u673a\u5668\u201d\uff0c\u5b83\u7531\u4e00\u4e2a\u9ed1\u5323\u5b50\u3001\u4e00\u5757\u8bb0\u5fc6\u677f\u3001\u4e00\u4e2a\u52a8\u4f5c\u6309\u94ae\u548c\u4e00\u4e2a\u91cd\u7f6e\u6309\u94ae\u7ec4\u6210\u3002\u673a\u5668\u5177\u6709\u4ee5\u4e0b\u5c5e\u6027\uff1a<\/p>\n<ol>\n<li style=\"text-align: justify; color: #000000;\">\u673a\u5668\u53ea\u6709\u4e00\u4e2a\u53ef\u914d\u7f6e\u7684\u53c2\u6570\uff1a\u5176\u6837\u672c\u7a7a\u95f4\u7684\u57fa\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N = \\{\\omega_1,\\cdots,\\omega_N\\}<\/span><\/li>\n<li style=\"text-align: justify; color: #000000;\">\u6309\u4e0b\u52a8\u4f5c\u6309\u94ae\u65f6\uff0c\u5b83\u5c06\u5728\u5c4f\u5e55\u4e0a\u663e\u793a <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N<\/span> \u4e2d\u7684\u4e00\u4e2a\u5143\u7d20<\/li>\n<li style=\"text-align: justify; color: #000000;\">\u5f53\u663e\u793a\u4e00\u4e2a\u7ed3\u679c\u65f6\uff0c\u5b83\u4f1a\u88ab\u5b58\u50a8\u5728\u8bb0\u5fc6\u677f\u4e2d\uff0c\u5728\u90a3\u91cc\u65f6\u6309\u4e0b\u52a8\u4f5c\u6309\u94ae\u5c06\u4e0d\u4f1a\u518d\u6b21\u663e\u793a\u76f8\u540c\u7684\u7ed3\u679c\u3002<\/li>\n<li style=\"text-align: justify; color: #000000;\">\u5982\u679c\u673a\u5668\u5df2\u7ecf\u663e\u793a\u4e86\u6240\u6709\u53ef\u80fd\u7684\u7ed3\u679c\uff0c\u5b83\u5c06\u51bb\u7ed3\u5e76\u4e0d\u518d\u663e\u793a\u4efb\u4f55\u5185\u5bb9\u3002<\/li>\n<li style=\"text-align: justify; color: #000000;\">\u91cd\u7f6e\u6309\u94ae\u4f1a\u6e05\u9664\u8bb0\u5fc6\u677f\u548c\u5c4f\u5e55\u4e0a\u7684\u663e\u793a\u5185\u5bb9\u3002<\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u4f7f\u7528\u8fd9\u53f0\u673a\u5668\uff0c\u6211\u4eec\u5c06\u8bbe\u8ba1\u4e00\u4e9b\u5b9e\u9a8c\u5e76\u5206\u6790\u5b83\u4eec\u7684\u6837\u672c\u7a7a\u95f4\u3002<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u5b9e\u9a8c1\uff08AORm\uff09\uff1a\u6267\u884c\u2014\u2014\u6309\u987a\u5e8f\u8bb0\u5f55\u2014\u2014\u91cd\u7f6e\uff0c\u91cd\u590dm\u6b21<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=406s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5c06\u673a\u5668\u914d\u7f6e\u4e3a<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega = N<\/span> \u5e76\u91cd\u590d <span class=\"katex-eq\" data-katex-display=\"false\">m\\leq N<\/span> \u6b21\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol>\n<li style=\"text-align: justify; color: #000000;\">\u6309\u4e0b\u52a8\u4f5c\u6309\u94ae<\/li>\n<li style=\"text-align: justify; color: #000000;\">\u5c06\u7ed3\u679c\u6309\u987a\u5e8f\u8bb0\u5f55\u5728\u5217\u8868\u4e2d<\/li>\n<li style=\"text-align: justify; color: #000000;\">\u91cd\u7f6e<\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u5b8c\u6210\u540e\uff0c\u6211\u4eec\u5c06\u83b7\u5f97\u4e00\u4e2a\u5305\u542b <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u4e2a <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N = \\{\\omega_1,\\cdots,\\omega_N\\}<\/span> \u5143\u7d20\u7684\u6709\u5e8f\u5217\u8868\u3002\u6b64\u5217\u8868\u53ef\u4ee5\u89e3\u91ca\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N<\/span> \u7684\u4e00\u4e2a m \u5143\u7ec4\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6b64\u5b9e\u9a8c\u7684\u6837\u672c\u7a7a\u95f4 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{AORm}<\/span> \u5c06\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{AORm}=\\Omega_N \\times \\cdots \\times \\Omega_N = \\Omega_N^m<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5f97\u5230 <span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega_{AORm}=\\#\\Omega_N^m = N^m<\/span>\u3002<\/p>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u5b9e\u9a8c2\uff08AOk\uff09\uff1a\u6267\u884c\u2014\u2014\u6309\u987a\u5e8f\u8bb0\u5f55\uff0c\u91cd\u590dk\u6b21<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=542s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u518d\u6b21\u5c06\u673a\u5668\u914d\u7f6e\u4e3a<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega = N<\/span> \u5e76\u91cd\u590d <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u6b21 (<span class=\"katex-eq\" data-katex-display=\"false\">k\\leq N<\/span>) \u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol>\n<li style=\"text-align: justify; color: #000000;\">\u6309\u4e0b\u52a8\u4f5c\u6309\u94ae\u3002<\/li>\n<li style=\"text-align: justify; color: #000000;\">\u5c06\u7ed3\u679c\u6309\u987a\u5e8f\u8bb0\u5f55\u5728\u5217\u8868\u4e2d\u3002<\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u5b8c\u6210\u540e\uff0c\u6211\u4eec\u5c06\u83b7\u5f97\u4e00\u4e2a\u5305\u542b <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u4e2a <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N = \\{\\omega_1,\\cdots,\\omega_N\\}<\/span> \u5143\u7d20\u7684\u6709\u5e8f\u5217\u8868\uff0c\u4f46\u5176\u4e2d\u7684\u4efb\u4f55\u5143\u7d20\u90fd\u4e0d\u4f1a\u4e0e\u5176\u524d\u9762\u7684\u5143\u7d20\u91cd\u590d\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u7531\u4e8e\u673a\u5668\u672c\u8d28\u4e0a\u4e0d\u4f1a\u504f\u5411\u4efb\u4f55\u53ef\u80fd\u7684\u7ed3\u679c\uff08\u56e0\u4e3a\u5b83\u662f\u5b8c\u7f8e\u968f\u673a\u7684\uff09\uff0c\u53ef\u4ee5\u5047\u8bbe\u5728\u7b2c\u4e00\u6b21\u6309\u4e0b\u52a8\u4f5c\u6309\u94ae\u65f6\u53d1\u751f\u4e86\u4e8b\u4ef6 <span class=\"katex-eq\" data-katex-display=\"false\">\\{\\omega_1\\}<\/span>\uff0c\u56e0\u6b64\u4e0b\u4e00\u6b21\u52a8\u4f5c\u7684\u6837\u672c\u7a7a\u95f4\u5e94\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N\\setminus\\{\\omega_1\\}<\/span>\u3002\u7c7b\u4f3c\u5730\uff0c\u53ef\u4ee5\u5047\u8bbe\u7b2c\u4e8c\u6b21\u6309\u4e0b\u52a8\u4f5c\u6309\u94ae\u65f6\u53d1\u751f\u4e86\u4e8b\u4ef6 <span class=\"katex-eq\" data-katex-display=\"false\">\\{\\omega_2\\}<\/span>\uff0c\u56e0\u6b64\u4e0b\u4e00\u6b21\u52a8\u4f5c\u7684\u6837\u672c\u7a7a\u95f4\u5e94\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">(\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}<\/span>\u3002\u5982\u679c\u7ee7\u7eed\u8fd9\u79cd\u65b9\u5f0f\uff0c\u5f53\u6211\u4eec\u8fdb\u884c\u7b2c k \u6b21\u52a8\u4f5c\u65f6\uff0c\u5176\u6837\u672c\u7a7a\u95f4\u5c06\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\cdots(\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}\\cdots)\\setminus\\{\\omega_{k-1}\\}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u6b64\u5b9e\u9a8c\u7684\u53ef\u80fd\u7ed3\u679c\u6837\u672c\u7a7a\u95f4\u5c06\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{AOk}= \\Omega \\times (\\Omega_N\\setminus\\{\\omega_1\\}) \\times ((\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}) \\times \\cdots \\times ((\\cdots(\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}\\cdots)\\setminus\\{\\omega_{k-1}\\}) <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u5982\u679c\u8ba1\u7b97\u6b64\u96c6\u5408\u7684\u57fa\u6570\uff0c\u6211\u4eec\u5c06\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega_{AOk}= N \\cdot (N-1) \\cdot (N-2) \\cdots [N-(k-1)]=\\displaystyle \\frac{N!}{(N-k)!}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6839\u636e\u8fd9\u4e00\u7ed3\u679c\uff0c\u6211\u4eec\u5f97\u51fa\u4ee5\u4e0b\u5b9a\u4e49\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; color: #800000; background-color: #dddddd;\"><strong>\u5b9a\u4e49<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; color: #000000; background-color: #ffffff;\">\u5b9a\u4e49 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u4e2a\u5143\u7d20\u6309 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u4e2a\u5206\u7ec4\u7684 <strong>\u53d8\u6362\u6570<\/strong> \u4e3a\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">(N)_k = \\displaystyle \\frac{N!}{(N-k)!}<\/span>\n<p>\u6839\u636e\u6b64\u5b9a\u4e49\uff0c\u4ee5\u53ca <span class=\"katex-eq\" data-katex-display=\"false\">0! =1<\/span> \u7684\u4e8b\u5b9e\uff0c\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u4e2a\u5143\u7d20\u4e4b\u95f4\u7684 <strong>\u6392\u5217\u6570<\/strong>\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">(N)_N = N!<\/span>\u3002<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u5b9e\u9a8c3\uff08ADk\uff09\uff1a\u6267\u884c\u2014\u2014\u65e0\u5e8f\u8bb0\u5f55\uff0c\u91cd\u590dk\u6b21<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=1204s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6b64\u5b9e\u9a8c\u4e0e\u524d\u4e00\u4e2a\u5b8c\u5168\u76f8\u540c\uff0c<\/span><\/strong><\/a>\u53ea\u4e0d\u8fc7\u73b0\u5728\u4e0d\u8bb0\u5f55 <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N<\/span> \u5143\u7d20\u51fa\u73b0\u7684\u987a\u5e8f\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e24\u4e2a\u5305\u542b\u76f8\u540c\u5143\u7d20\u4f46\u987a\u5e8f\u4e0d\u540c\u7684 k \u5143\u7ec4\u73b0\u5728\u88ab\u89c6\u4e3a\u540c\u4e00\u4e2a\u3002\u56e0\u6b64\uff0c\u5229\u7528\u4ece\u5b9e\u9a8c AOk \u83b7\u5f97\u7684\u6bcf\u4e2a k \u5143\u7ec4\u53ef\u4ee5\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">(k)_k=k!<\/span> \u79cd\u4e0d\u540c\u7684\u65b9\u5f0f\u5199\u51fa\uff0c\u5c06\u5f97\u5230\u6b64\u5b9e\u9a8c\u6837\u672c\u7a7a\u95f4\u7684\u57fa\u6570\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega_{ADk} = \\displaystyle \\frac{\\#\\Omega_{AOk}}{(k)_k} = \\frac{(N)_k}{k!} = \\frac{N!}{k!(N-k)!} <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6839\u636e\u6b64\u7ed3\u679c\uff0c\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u5b9a\u4e49\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; color: #800000; background-color: #dddddd;\"><strong>\u5b9a\u4e49<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; color: #000000; background-color: #ffffff;\">\u5b9a\u4e49 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u4e2a\u5143\u7d20\u6309 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u4e2a\u5206\u7ec4\u7684 <strong>\u7ec4\u5408\u6570<\/strong> \u4e3a\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{N}\\choose{k}}= \\frac{N!}{k!(N-k)!} <\/span>\n<p>\u8fd9\u4ee3\u8868\u4e86\u53ef\u4ee5\u4ece\u5305\u542b N \u4e2a\u5143\u7d20\u7684\u96c6\u5408\u4e2d\u62bd\u53d6 k \u4e2a\u5143\u7d20\u5f62\u6210\u7684\u5b50\u96c6\u6570\u91cf\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u901a\u8fc7\u6392\u5217\u3001\u53d8\u6362\u548c\u7ec4\u5408\u7684\u8ba1\u6570\u6280\u672f\uff0c\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u6d4b\u91cf\u5404\u79cd\u96c6\u5408\u7684\u5927\u5c0f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8ba1\u6570\u6280\u672f\uff1a\u6392\u5217\u3001\u53d8\u6362\u548c\u7ec4\u5408 \u6458\u8981\u5728\u6982\u7387\u7814\u7a76\u4e2d\uff0c\u8ba1\u6570\u6280\u672f\u662f\u6d4b\u91cf\u6837\u672c\u7a7a\u95f4\u548c\u5f85\u6d4b\u4e8b\u4ef6\u57fa\u6570\u7684\u57fa\u672c\u5de5\u5177\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7531\u4e8e\u5728\u7b49\u6982\u7387\u7ed3\u679c\u7684\u5b9e\u9a8c\u4e2d\u4f7f\u7528\u65b9\u4fbf\uff0c\u7ec4\u5408\u3001\u53d8\u6362\u548c\u6392\u5217\u6280\u672f\u662f\u6700\u5e38\u7528\u7684\u3002\u901a\u8fc7\u5c06\u6982\u7387\u6d4b\u91cf\u4e3a\u76f8\u5bf9\u9891\u7387\u7684\u6781\u9650\uff0c\u53ef\u4ee5\u5c06\u4e8b\u4ef6\u7684\u6982\u7387\u8868\u793a\u4e3a\u57fa\u6570\u7684\u5546\u3002\u56e0\u6b64\uff0c\u6982\u7387\u8ba1\u7b97\u5f52\u7ed3\u4e3a\u8ba1\u7b97\u6837\u672c\u7a7a\u95f4\u548c\u5f85\u6d4b\u4e8b\u4ef6\u7684\u57fa\u6570\u3002\u5728\u8fd9\u65b9\u9762\uff0c\u901a\u8fc7\u7b49\u6982\u7387\u7ed3\u679c\u5b9e\u9a8c\u83b7\u5f97\u7684\u8ba1\u6570\u6280\u672f\u5bf9\u4e8e\u6982\u7387\u7814\u7a76\u81f3\u5173\u91cd\u8981\u3002\u901a\u8fc7\u5b9a\u4e49\u53d8\u6362\u3001\u7ec4\u5408\u548c\u6392\u5217\uff0c\u53ef\u4ee5\u6709\u6548\u4e14\u7cbe\u786e\u5730\u6d4b\u91cf\u96c6\u5408\u7684\u5927\u5c0f\u3002\u672c\u8bfe\u5c06\u4ecb\u7ecd\u4e00\u4e9b\u5177\u6709\u7b49\u6982\u7387\u7ed3\u679c\u7684\u5b9e\u9a8c\uff0c\u5e76\u5206\u6790\u5176\u6837\u672c\u7a7a\u95f4\u4ee5\u5f15\u5165\u8ba1\u6570\u6280\u672f\u3002\u4f7f\u7528\u8fd9\u4e9b\u5de5\u5177\uff0c\u53ef\u4ee5\u6d4b\u91cf\u5404\u79cd\u96c6\u5408\u7684\u5927\u5c0f\u5e76\u8ba1\u7b97\u7b49\u6982\u7387\u7ed3\u679c\u5b9e\u9a8c\u4e2d\u7684\u4e8b\u4ef6\u6982\u7387\u3002 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