{"id":2574,"date":"2022-04-29T11:46:03","date_gmt":"2022-04-29T09:46:03","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/variace-s-opakovanim-vypocet-a-vzorovy-priklad\/"},"modified":"2022-04-29T12:51:34","modified_gmt":"2022-04-29T10:51:34","slug":"variace-s-opakovanim-zakladni-vzorec-vzorovy-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/variace-s-opakovanim-zakladni-vzorec-vzorovy-priklad\/","title":{"rendered":"Variace s opakov\u00e1n\u00edm &#8211; z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p>VARIACE S OPAKOV\u00c1N\u00cdM vyu\u017eijeme k v\u00fdpo\u010dtu v p\u0159\u00edpad\u011b, \u017ee se <strong>prvky mohou opakovat<\/strong><\/p>\n<ul>\n<li>P\u0159i po\u010d\u00edt\u00e1n\u00ed p\u0159\u00edklad\u016f na VARIACE S OPAKOV\u00c1N\u00cdM ji\u017e nemus\u00ed platit pravidlo, \u017ee <strong><em>k\u2264n<\/em><\/strong>. Pro\u010d? <strong>Po\u010det prvk\u016f, ze kter\u00fdch m\u016f\u017eeme vyb\u00edrat se toti\u017e nem\u011bn\u00ed, ale z\u016fst\u00e1v\u00e1 neust\u00e1le stejn\u00fd<\/strong> &#8211; to je d\u00e1no t\u00edm, \u017ee se PRVKY MOHOU OPAKOVAT. Mno\u017eina prvk\u016f se tud\u00ed\u017e nem\u011bn\u00ed!<\/li>\n<li>Tak\u00e9 vzorec pro v\u00fdpo\u010det VARIAC\u00cd S OPAKOV\u00c1N\u00cdM je jin\u00fd, ne\u017e pro v\u00fdpo\u010det VARIAC\u00cd BEZ OPAKOV\u00c1N\u00cd.<\/li>\n<li>k-prvkov\u00e9 variace z n-prvk\u016f, kde se m\u016f\u017ee prvek z n mo\u017einy opakovat, vypo\u010d\u00edt\u00e1me pomoc\u00ed vzorc:<\/li>\n<\/ul>\n<p>$$V\u00b4(k,n)={n}^{k}$$<\/p>\n<ul>\n<li>Ur\u010dit\u011b jste si tak\u00e9 pov\u0161imli, \u017ee zat\u00edmco VARIACE BEZ OPAKOV\u00c1N\u00cd zna\u010d\u00edme <strong><em>V<\/em><\/strong>,<\/li>\n<li>VARIACE S OPAKOV\u00c1N\u00cdM zna\u010d\u00edme <em><strong>V\u00b4<\/strong><\/em><\/li>\n<li>Variace s opakov\u00e1n\u00edm vyu\u017eijeme p\u0159i po\u010d\u00edt\u00e1n\u00ed kombinac\u00ed hesla \u010di p\u0159i sestavov\u00e1n\u00ed \u010d\u00edsel z cifer kter\u00e9 se mohou v \u010d\u00edsle opakovat<\/li>\n<\/ul>\n<p>Vzorov\u00fd p\u0159\u00edklad:<\/p>\n<p>Kolik \u0161esticifern\u00fdch \u010d\u00edsel lze sestavit z \u010d\u00edslic {1, 3, 6, 8}, jestli\u017ee se mohou \u010d\u00edslice opakovat?<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p style=\"text-align: center\">M\u00e1me mno\u017einu o 4 prvc\u00edch a vyb\u00edr\u00e1me z n\u00ed 6 prvk\u016f \u21d2<em><strong> k=6, n=4<\/strong><\/em><\/p>\n<p style=\"text-align: center\">Dosad\u00edme tedy do vzorce pro Variace s opakov\u00e1n\u00edm<\/p>\n<p>$$V\u00b4(k,n)={n}^{k}$$<\/p>\n<p style=\"text-align: center\">a dostaneme:<\/p>\n<p>$$V\u00b4(6,4)={4}^{6}=4096$$<\/p>\n<p style=\"text-align: center\">Z \u010d\u00edslic {1, 3, 6, 8} lze sestavit 4096 \u0161esticifern\u00fdch \u010d\u00edsel, jestli\u017ee se mohou \u010d\u00edslice opakovat.<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2574","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>Variace s opakov\u00e1n\u00edm - 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\/variace-s-opakovanim-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=\"Variace s opakov\u00e1n\u00edm - z\u00e1kladn\u00ed vzorec + vzorov\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"VARIACE S OPAKOV\u00c1N\u00cdM vyu\u017eijeme k v\u00fdpo\u010dtu v p\u0159\u00edpad\u011b, \u017ee se prvky mohou opakovat P\u0159i po\u010d\u00edt\u00e1n\u00ed p\u0159\u00edklad\u016f na VARIACE S OPAKOV\u00c1N\u00cdM ji\u017e nemus\u00ed platit pravidlo, \u017ee k\u2264n. 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