{"id":7209,"date":"2011-11-27T17:45:02","date_gmt":"2011-11-27T17:45:02","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7209"},"modified":"2021-12-28T13:04:58","modified_gmt":"2021-12-28T13:04:58","slug":"direcao-de-clube","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7209","title":{"rendered":"Dire\u00e7\u00e3o de um clube"},"content":{"rendered":"<p><ul id='GTTabs_ul_7209' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7209' class='GTTabs_curr'><a  id=\"7209_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7209' ><a  id=\"7209_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7209'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um grupo de 35 jovens, dos quais 15 s\u00e3o raparigas, decide formar um clube cuja dire\u00e7\u00e3o ser\u00e1 constitu\u00edda por 5 elementos:<\/p>\n<ul>\n<li>um presidente (rapaz);<\/li>\n<li>um vice-presidente (rapariga);<\/li>\n<li>um secret\u00e1rio (rapariga);<\/li>\n<li>um tesoureiro (qualquer g\u00e9nero);<\/li>\n<li>um rela\u00e7\u00f5es p\u00fablicas (qualquer g\u00e9nero).<\/li>\n<\/ul>\n<p>Qual \u00e9 o n\u00famero de dire\u00e7\u00f5es diferentes poss\u00edveis?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7209' onClick='GTTabs_show(1,7209)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7209'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Pela ordem indicada no enunciado, cada um dos cargos pode ser assumido no seguinte n\u00famero de maneiras diferentes:<\/p>\n<ul>\n<li>presidente: ${}^{20}{{C}_{1}}=20$<\/li>\n<li>vice-presidente: ${}^{15}{{C}_{1}}=15$<\/li>\n<li>secret\u00e1rio: ${}^{14}{{C}_{1}}=14$<\/li>\n<li>tesoureiro: ${}^{32}{{C}_{1}}=32$<\/li>\n<li>rela\u00e7\u00f5es p\u00fablicas: ${}^{31}{{C}_{1}}=31$<\/li>\n<\/ul>\n<p><strong>Nota<\/strong>: em rela\u00e7\u00e3o aos dois \u00faltimos cargos, esse n\u00famero poder\u00e1 ser expresso por ${}^{32}{{C}_{2}}\\times {{P}_{2}}=496\\times 2=992$. (Porqu\u00ea)<\/p>\n<p>Assim, pode obter-se o seguinte n\u00famero de dire\u00e7\u00f5es diferentes: $$N={}^{20}{{C}_{1}}\\times {}^{15}{{C}_{1}}\\times {}^{14}{{C}_{1}}\\times {}^{32}{{C}_{1}}\\times {}^{31}{{C}_{1}}=20\\times 15\\times 14\\times 32\\times 31=4166400$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7209' onClick='GTTabs_show(0,7209)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um grupo de 35 jovens, dos quais 15 s\u00e3o raparigas, decide formar um clube cuja dire\u00e7\u00e3o ser\u00e1 constitu\u00edda por 5 elementos: um presidente (rapaz); um vice-presidente (rapariga); um secret\u00e1rio (rapariga); um&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19174,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255],"series":[],"class_list":["post-7209","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-probabilidades-e-combinatoria","tag-12-o-ano","tag-analise-combinatoria"],"views":1623,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat65.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7209","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7209"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7209\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7209"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7209"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}