{"id":2492,"date":"2022-04-25T16:44:11","date_gmt":"2022-04-25T16:44:11","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/permutace-bez-opakovani-zakladni-vzorec-vzorovy-priklad\/"},"modified":"2022-04-25T17:41:51","modified_gmt":"2022-04-25T17:41:51","slug":"permutace-bez-opakovani-zakladni-vzorec-vzorovy-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/permutace-bez-opakovani-zakladni-vzorec-vzorovy-priklad\/","title":{"rendered":"Permutace bez opakov\u00e1n\u00ed &#8211; z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p>Kdy vyu\u017eijeme vzore\u010dek pro PERMUTACE BEZ OPAKOV\u00c1N\u00cd a jak v\u016fbec vypad\u00e1?<\/p>\n<ul>\n<li>Permutace bez opakov\u00e1n\u00ed jsou <strong>uspo\u0159\u00e1dan\u00e9 n-tice<\/strong> z t\u011bchto <strong><em>n<\/em><\/strong> prvk\u016f, p\u0159i\u010dem\u017e plat\u00ed, \u017ee <strong>ka\u017ed\u00fd prvek se v dan\u00e9 n-tici vyskytuje pouze jednou<\/strong>. Jednotliv\u00e9 permutace t\u011bchto prvk\u016f se od sebe li\u0161\u00ed po\u0159ad\u00edm prvk\u016f. Co to tedy znamen\u00e1?<\/li>\n<li><strong>Hled\u00e1me v\u0161echny zp\u016fsoby, kter\u00fdmi lze dan\u00e9 prvky mo\u017en\u00e9 uspo\u0159\u00e1dat.<\/strong> Nap\u0159\u00edklad: kolika zp\u016fsoby se d\u00e1 uspo\u0159\u00e1dat na poli\u010dku 5 knih, kolik \u010dty\u0159cifern\u00fdch \u010d\u00edsel sestav\u00edme ze 4 r\u016fzn\u00fdch cifer, kolika zp\u016fsoby m\u016f\u017eeme uspo\u0159\u00e1dat do kruhu 8 jedinc\u016f, kolik n\u00e1hrdeln\u00edk\u016f lze vytvo\u0159it z deseti r\u016fzn\u00fdch kor\u00e1lk\u016f atd.<\/li>\n<li><em><strong>k=n<\/strong><\/em>, nerozli\u0161ujeme tedy mezi ozna\u010den\u00edm <em><strong>k<\/strong><\/em> a<strong><em> n<\/em><\/strong>, proto\u017ee si vysta\u010d\u00edme pouze s <em><strong>n<\/strong><\/em>.<\/li>\n<li>Vzorec pro\u010d v\u00fdpo\u010det permutace bez opakov\u00e1n\u00ed vypad\u00e1:<\/li>\n<\/ul>\n<p>$$P(n)=n!$$<\/p>\n<p><strong>Vzorov\u00fd p\u0159\u00edklad:<\/strong><\/p>\n<p>Kolika zp\u016fsoby lze deset d\u011bt\u00ed:<\/p>\n<p>a) poskl\u00e1dat do \u0159ady?<\/p>\n<p>b) poskl\u00e1dat do \u0159ady tak, aby byla Ani\u010dka na kraji?<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>a) Pot\u0159ebujeme poskl\u00e1dat do \u0159ady deset d\u011bt\u00ed, po\u010det prvk\u016f, ze kter\u00fdch tvo\u0159\u00edme permutace je tedy rovn\u00fd 10.<\/p>\n<p style=\"text-align: center\"><em><strong>n=10<\/strong><\/em> \u21d2 <em><strong>P(n)=n!<\/strong><\/em> \u21d2 <strong><em>P(10)=10!<\/em><em>=3 628 800<\/em><\/strong><\/p>\n<p>b) V tomto p\u0159\u00edpad\u011b budeme po\u010d\u00edtat permutace pouze z 9 d\u011bt\u00ed. Ale proto\u017ee Ani\u010dka se m\u016f\u017ee postavit doleva nebo doprava, mus\u00edme celou permutaci n\u00e1sobit dv\u011bma.<\/p>\n<p style=\"text-align: center\"><em><strong>n=9<\/strong><\/em>\u00a0\u21d2 <em><strong>P(n)=n!<\/strong><\/em> \u21d2 <strong><em>P(9)=9!<\/em><\/strong><\/p>\n<p style=\"text-align: center\"><strong><em>9!\u22c52=725 760<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2492","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Permutace bez opakov\u00e1n\u00ed - z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad | Studijni-svet.cz<\/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:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/permutace-bez-opakovani-zakladni-vzorec-vzorovy-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Permutace bez opakov\u00e1n\u00ed - z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Kdy vyu\u017eijeme vzore\u010dek pro PERMUTACE BEZ OPAKOV\u00c1N\u00cd a jak v\u016fbec vypad\u00e1? Permutace bez opakov\u00e1n\u00ed jsou uspo\u0159\u00e1dan\u00e9 n-tice z t\u011bchto n prvk\u016f, p\u0159i\u010dem\u017e plat\u00ed, \u017ee ka\u017ed\u00fd prvek se v dan\u00e9 n-tici vyskytuje pouze jednou. Jednotliv\u00e9 permutace t\u011bchto prvk\u016f se od sebe li\u0161\u00ed po\u0159ad\u00edm prvk\u016f. Co to tedy znamen\u00e1? Hled\u00e1me v\u0161echny zp\u016fsoby, kter\u00fdmi lze dan\u00e9 prvky mo\u017en\u00e9 ... 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Permutace bez opakov\u00e1n\u00ed jsou uspo\u0159\u00e1dan\u00e9 n-tice z t\u011bchto n prvk\u016f, p\u0159i\u010dem\u017e plat\u00ed, \u017ee ka\u017ed\u00fd prvek se v dan\u00e9 n-tici vyskytuje pouze jednou. Jednotliv\u00e9 permutace t\u011bchto prvk\u016f se od sebe li\u0161\u00ed po\u0159ad\u00edm prvk\u016f. Co to tedy znamen\u00e1? Hled\u00e1me v\u0161echny zp\u016fsoby, kter\u00fdmi lze dan\u00e9 prvky mo\u017en\u00e9 ... 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