{"id":4777,"date":"2022-09-02T15:13:51","date_gmt":"2022-09-02T13:13:51","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kombinatorika-priklad-1\/"},"modified":"2022-09-02T15:13:51","modified_gmt":"2022-09-02T13:13:51","slug":"kombinatorika-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kombinatorika-priklad-1\/","title":{"rendered":"Kombinatorika &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Pro vstup do m\u00edstnosti je pot\u0159eba otev\u0159\u00edt 2 dve\u0159e. U obou se nejd\u0159\u00edve mus\u00ed zadat \u010dty\u0159m\u00edstn\u00fd k\u00f3d, kter\u00fd m\u016f\u017ee obsahovat \u010d\u00edsla 0-9.<br \/>D\u00e1le v\u00edme, \u017ee:<br \/>a) K\u00f3d prvn\u00edch dve\u0159\u00ed obsahuje v\u0161echny \u010dty\u0159i \u010d\u00edsla 1, 2, 3, 4<br \/>b) K\u00f3d druh\u00fdch spl\u0148uje hned t\u0159i podm\u00ednky: &#8211; neobsahuje \u017e\u00e1dn\u00e9 \u010d\u00edslo, kter\u00e1 je v k\u00f3du u prvn\u00edch dve\u0159\u00ed &#8211; obsahuje dvakr\u00e1t \u010d\u00edslo 0, a to na 2. a 3. m\u00edst\u011b &#8211; krom\u011b \u010d\u00edsla 0 neobsahuje \u017e\u00e1dn\u00e9 jin\u00e9 \u010d\u00edslo dvakr\u00e1t<br \/>&nbsp; <br \/><strong>Zjist\u011bte, jak\u00fd je po\u010det v\u0161ech mo\u017enost\u00ed spl\u0148uj\u00edc\u00edch podm\u00ednky zad\u00e1n\u00ed pro k\u00f3d:<\/strong><br \/><strong>a) u prvn\u00edch dve\u0159\u00ed<\/strong><\/p>\n<p><strong>b) u druh\u00fdch dve\u0159\u00ed<\/strong><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p><em>a)K\u00f3d u prvn\u00edch dve\u0159\u00ed<\/em><\/p>\n<p>1) K\u00f3d u prvn\u00edch dve\u0159\u00ed m\u00e1 4 m\u00edstn\u00fd k\u00f3d, kter\u00fd obsahuje tato \u010d\u00edsla: 1, 2, 3 a 4. Jedn\u00e1 se o situaci, kdy je po\u0159ad\u00ed \u010d\u00edsel relevantn\u00ed, jde o variace. A to konkr\u00e9tn\u011b variace bez opakov\u00e1n\u00ed, proto\u017ee maj\u00ed b\u00fdt obsa\u017eeny v\u0161echny \u010dty\u0159i cifry.<\/p>\n<p>2) V z\u00e1vorce je specifikov\u00e1no, kolik m\u00e1me mo\u017enost\u00ed, a kolik cifer mus\u00edme obsadit. D\u00e1le \u010d\u00edsla zna\u010d\u00ed mo\u017enosti, kter\u00e9 m\u00e1me. Pochopiteln\u011b s u\u017eit\u00edm \u010d\u00edsel n\u00e1m p\u0159i ka\u017ed\u00e9 dal\u0161\u00ed obsazen\u00e9 cif\u0159e mo\u017enosti o 1 ub\u00fdvaj\u00ed.<br \/><em><strong>V(a) (4; 4) = 4 \u00b7 3 \u00b7 2 \u00b7 1 = 24<\/strong><\/em><\/p>\n<p><em>b) K\u00f3d u druh\u00fdch dve\u0159\u00ed<\/em><\/p>\n<p>1) K\u00f3d u druh\u00fdch dve\u0159\u00ed m\u00e1 tak\u00e9 \u010dty\u0159i cifry. Nuly zde maj\u00ed jasnou pozici, a to na druh\u00e9m a t\u0159et\u00edm m\u00edst\u011b. Na prvn\u00edm a \u010dtvrt\u00e9m m\u00edst\u011b se tak mohou objevit \u010d\u00edsla 5, 6, 7, 8 nebo 9. I zde budeme po\u010d\u00edtat pomoc\u00ed variace (pouze ze 2 cifer), z\u00e1le\u017e\u00ed n\u00e1m na po\u0159ad\u00ed cifer.<\/p>\n<p>2) V z\u00e1vorce m\u00e1me specifikov\u00e1no, \u017ee m\u00e1me na v\u00fdb\u011br z 5 \u010d\u00edsel a pot\u0159ebujeme obsadit pouze 2 cifry. P\u0159i prvn\u00ed cif\u0159e m\u00e1me v\u0161ech 5 mo\u017enost\u00ed a u posledn\u00ed cifry se n\u00e1m tato mo\u017enost o 1 ji\u017e obsazenou sn\u00ed\u017e\u00ed. Druh\u00e9 a t\u0159et\u00ed m\u00edst\u011b je specifikov\u00e1no. <br \/><em><strong>V(b) (5; 2) = 5 \u00b7 1 \u00b7 1 \u00b7 4 = 20<\/strong><\/em><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 6-8 minut<br \/>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<br \/>&nbsp; <\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4777","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>Kombinatorika - p\u0159\u00edklad 1 | 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\/kombinatorika-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kombinatorika - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Pro vstup do m\u00edstnosti je pot\u0159eba otev\u0159\u00edt 2 dve\u0159e. 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