{"id":9855,"date":"2022-01-30T16:10:48","date_gmt":"2022-01-30T10:40:48","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9855"},"modified":"2022-01-30T16:10:51","modified_gmt":"2022-01-30T10:40:51","slug":"prove-that-value-of-zero-factorial-is-1","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-value-of-zero-factorial-is-1\/","title":{"rendered":"Prove that value of zero factorial is 1."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>We have, P(n, r) = \\(n!\\over (n &#8211; r)!\\)<\/p>\n<p>Putting r = n,<\/p>\n<p>\\(\\implies\\)\u00a0 P(n, n) = \\(n!\\over 0!\\)<\/p>\n<p>\\(\\implies\\)\u00a0 n! = \\(n!\\over 0!\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[ \\(\\because\\)\u00a0 P(n, n) = n! ]<\/p>\n<p>\\(\\implies\\)\u00a0 0! = \\(n!\\over n!\\)\u00a0 = 1<\/p>\n<p>Hence, Proved.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : We have, P(n, r) = \\(n!\\over (n &#8211; r)!\\) Putting r = n, \\(\\implies\\)\u00a0 P(n, n) = \\(n!\\over 0!\\) \\(\\implies\\)\u00a0 n! = \\(n!\\over 0!\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[ \\(\\because\\)\u00a0 P(n, n) = n! ] \\(\\implies\\)\u00a0 0! = \\(n!\\over n!\\)\u00a0 = 1 Hence, Proved.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,47],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Prove that value of zero factorial is 1. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/prove-that-value-of-zero-factorial-is-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that value of zero factorial is 1. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, P(n, r) = (n!over (n &#8211; r)!) 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