{"id":7217,"date":"2011-11-28T15:47:06","date_gmt":"2011-11-28T15:47:06","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7217"},"modified":"2022-01-25T23:00:00","modified_gmt":"2022-01-25T23:00:00","slug":"parque-de-estacionamento","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7217","title":{"rendered":"Parque de estacionamento"},"content":{"rendered":"<p><ul id='GTTabs_ul_7217' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7217' class='GTTabs_curr'><a  id=\"7217_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7217' ><a  id=\"7217_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_7217'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7218\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7218\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto.jpg\" data-orig-size=\"500,333\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Parque de estacionamento\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto.jpg\" class=\"alignright wp-image-7218\" title=\"Parque de estacionamento\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto.jpg\" alt=\"\" width=\"300\" height=\"200\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto.jpg 500w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto-300x199.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto-150x99.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/parquemoto-400x266.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Seis amigos chegam \u00e0 escola conduzindo cada um a sua motorizada e encontram os dez lugares do parque de estacionamento vazios.<\/p>\n<ol>\n<li>De quantas formas podem estacionar as motorizadas se n\u00e3o houver qualquer restri\u00e7\u00e3o?<\/li>\n<li>Supondo que os lugares de estacionamento lhes foram atribu\u00eddos ao acaso, qual a probabilidade de ficarem todos juntos, num dos extremos do estacionamento?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7217' onClick='GTTabs_show(1,7217)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7217'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Seis dos 10 lugares de estacionamento podem ser selecionados de $^{10}{{C}_{6}}$ maneiras diferentes.<br \/>\nPara cada uma destas maneiras, os seis amigos podem estacionar as suas motorizadas de ${{P}_{6}}$ modos diferentes.<br \/>\nPortanto, n\u00e3o havendo qualquer restri\u00e7\u00e3o, os seis amigos podem estacionar as motorizadas de\u00a0$$N{{=}^{10}}{{C}_{6}}\\times {{P}_{6}}{{=}^{10}}{{A}_{6}}=10\\times 9\\times 8\\times 7\\times 6\\times 5=151200$$ modos diferentes.<\/li>\n<li>H\u00e1 dois extremos, esquerdo e direito, onde podem estacionar todos juntos.<br \/>\nPara cada uma destas situa\u00e7\u00f5es, podem estacionar de ${{P}_{6}}$ modos diferentes.<br \/>\nAssim, o n\u00famero de casos\u00a0favor\u00e1veis \u00e9 $NCF=2\\times {{P}_{6}}$.<\/p>\n<p>Portanto, a probabilidade pedida \u00e9 $$p=\\frac{2\\times {{P}_{6}}}{^{10}{{C}_{6}}\\times {{P}_{6}}}=\\frac{2}{^{10}{{C}_{6}}}=\\frac{2\\times 4!\\times 6!}{10\\times 9\\times 8\\times 7\\times 6\\times 5\\times 4!}=\\frac{2\\times 6\\times 5\\times 4\\times 3\\times 2\\times 1}{10\\times 9\\times 8\\times 7\\times 6\\times 5}=\\frac{1}{105}$$A probabilidade pedida tamb\u00e9m \u00e9 dada por (qual \u00e9 o racioc\u00ednio) $$p=\\frac{2}{^{10}{{C}_{6}}}=\\frac{1}{105}$$<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7217' onClick='GTTabs_show(0,7217)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Seis amigos chegam \u00e0 escola conduzindo cada um a sua motorizada e encontram os dez lugares do parque de estacionamento vazios. De quantas formas podem estacionar as motorizadas se n\u00e3o houver&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21042,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255,215],"series":[],"class_list":["post-7217","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","tag-probabilidade"],"views":3259,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/12V1Pag176-55_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7217","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=7217"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7217\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21042"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7217"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}