{"id":7185,"date":"2011-11-20T22:40:05","date_gmt":"2011-11-20T22:40:05","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7185"},"modified":"2022-01-25T22:13:49","modified_gmt":"2022-01-25T22:13:49","slug":"um-grupo-de-amigos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7185","title":{"rendered":"Um grupo de amigos"},"content":{"rendered":"<p><ul id='GTTabs_ul_7185' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7185' class='GTTabs_curr'><a  id=\"7185_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7185' ><a  id=\"7185_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_7185'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/cinema2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7186\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7186\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/cinema2.jpg\" data-orig-size=\"358,208\" 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=\"Cinema\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/cinema2.jpg\" class=\"alignright wp-image-7186\" title=\"Cinema\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/cinema2.jpg\" alt=\"\" width=\"240\" height=\"139\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/cinema2.jpg 358w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/cinema2-300x174.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/cinema2-150x87.jpg 150w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Um grupo de amigos, constitu\u00eddo por tr\u00eas rapazes e duas raparigas, vai ao cinema e ocupa cinco lugares consecutivos.<\/p>\n<ol>\n<li>De quantos modos distintos se podem sentar?<\/li>\n<li>E se cada uma das raparigas ficar num dos extremos?<\/li>\n<li>E se as raparigas n\u00e3o se sentarem nos extremos?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7185' onClick='GTTabs_show(1,7185)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7185'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><!--more--><\/p>\n<ol>\n<li>Os cinco amigos podem sentar-se nos cinco lugares de ${}^{5}{{A}_{5}}={{P}_{5}}=5\\times 4\\times 3\\times 2\\times 1=120$ modos diferentes.<br \/>\n\u00ad<\/li>\n<li>Se cada rapariga ficar num dos extremos, estas podem sentar-se de\u00a0$2={{P}_{2}}$ maneiras diferentes e, para cada uma destas maneiras, os rapazes podem sentar-se de ${}^{3}{{A}_{3}}={{P}_{3}}=3\\times 2\\times 1=6$ maneiras diferentes.<br \/>\nAssim, nestas condi\u00e7\u00f5es, os cinco amigos podem sentar-se de $N={{P}_{2}}\\times {{P}_{3}}=2\\times 6=12$ modos diferentes.<br \/>\n\u00ad<\/li>\n<li>Se as raparigas n\u00e3o se sentarem nos extremos, h\u00e1 tr\u00eas lugares dispon\u00edveis para se sentarem, os quais podem ser selecionados em grupos de dois de ${}^{3}{{C}_{2}}=3$ maneiras diferentes. Desta forma, as raparigas podem sentar-se de ${}^{3}{{C}_{2}}\\times {{P}_{2}}={}^{3}{{A}_{2}}$ maneiras diferentes e, para cada uma destas maneiras, os 3 rapazes podem sentar-se nos restantes tr\u00eas lugares de ${{P}_{3}}=3\\times 2\\times 1=6$ maneiras diferentes.<br \/>\nAssim, nestas condi\u00e7\u00f5es, os cinco amigos podem sentar-se de $N={}^{3}{{A}_{2}}\\times {{P}_{3}}=3\\times 2\\times 6=36$ modos diferentes.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7185' onClick='GTTabs_show(0,7185)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um grupo de amigos, constitu\u00eddo por tr\u00eas rapazes e duas raparigas, vai ao cinema e ocupa cinco lugares consecutivos. De quantos modos distintos se podem sentar? E se cada uma das&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21034,"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-7185","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":3243,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/12V1Pag174-43_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7185","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=7185"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7185\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21034"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7185"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}