{"id":9938,"date":"2021-03-30T15:24:19","date_gmt":"2021-03-30T13:24:19","guid":{"rendered":"http:\/\/nosolomates.es\/?page_id=9938"},"modified":"2021-03-30T15:24:20","modified_gmt":"2021-03-30T13:24:20","slug":"variaciones","status":"publish","type":"page","link":"http:\/\/nosolomates.es\/?page_id=9938","title":{"rendered":"Variaciones"},"content":{"rendered":"<p>Herramienta para calcular el n\u00famero de variaciones de n elementos en grupos de k elementos. Introduce el n\u00famero en la caja y pulsa &#8220;Calcular&#8221;. Para ver los agrupamientos, pulsa &#8220;Agrupamientos&#8221;.<\/p>\n<p><center><\/p>\n<div id=\"utilidades\"><h7><iframe loading=\"lazy\" src=\"web\/variaciones.htm\" scrolling=\"auto\" width=\"470\" height=\"600\" frameborder=\"0\"><\/p>\n<p>Texto alternativo para browsers que no aceptan iframes.<\/p>\n<p><\/iframe><\/h7><\/div>\n<p><\/center><\/p>\n<h1>Explicaci\u00f3n:<\/h1>\n<p>Las <b>variaciones<\/b> de n elementos tomados en grupos de k son las diferentes formas de ordenar k elementos elegidos de un conjunto de n elementos. Por ejemplo, si tenemos 3 elementos, A, B y C, y queremos hacer grupos de dos elementos <u>sin que se repitan<\/u>, podemos hacerlo de 6 formas:<\/p>\n<p><center>AB&nbsp;&nbsp;AC&nbsp;&nbsp;BA&nbsp;&nbsp;BC&nbsp;&nbsp;CA&nbsp;&nbsp;CB<\/center><br \/>\nEsto es porque, en el primer lugar, podemos colocar cualquiera de los 3 elementos (A, B o C); como no se pueden repetir, en el segundo lugar podemos poner uno de los dos que no hemos puesto. Esto es, 3\u00b72 = 6.<br \/>\nEn general, para n elementos tomados de k en k, la f\u00f3rmula es:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/nosolomates.es\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_969_f1b915724dc8fe60584b4310c44ef634.png\" style=\"vertical-align:-31px; display: inline-block ;\" alt=\"V(n,k)={n!}\/{(n-k)!}\" title=\"V(n,k)={n!}\/{(n-k)!}\"\/><\/center><\/p>\n<p>Si <u>se pueden repetir<\/u>, entonces tendr\u00edamos 9 formas de hacerlo:<br \/>\n<center>AA&nbsp;&nbsp;AB&nbsp;&nbsp;AC&nbsp;&nbsp;BA&nbsp;&nbsp;BB&nbsp;&nbsp;BC&nbsp;&nbsp;CA&nbsp;&nbsp;CB&nbsp;&nbsp;CC<\/center><br \/>\nYa que en este caso, en primer lugar podemos poner cualquiera de los 3 elementos y, en el segundo, tambi\u00e9n cualquiera de los 3 elementos, es decir, 3\u00b73 = 9.<br \/>\nEn general, para n elementos tomados de k en k, con repetici\u00f3n, la f\u00f3rmula es:<br \/>\n<center><img decoding=\"async\" src=\"http:\/\/nosolomates.es\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_986_f23a70c5beef0fa491988ab71bcf49b0.png\" style=\"vertical-align:-14px; display: inline-block ;\" alt=\"VR(n,k)=n^k\" title=\"VR(n,k)=n^k\"\/><\/center><\/p>\n<div>\n&nbsp;<\/div>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-official sd-sharing\"><div class=\"sd-content\"><ul><li class=\"share-facebook\"><div class=\"fb-share-button\" data-href=\"http:\/\/nosolomates.es\/?page_id=9938\" data-layout=\"button_count\"><\/div><\/li><li class=\"share-twitter\"><a href=\"https:\/\/twitter.com\/share\" class=\"twitter-share-button\" data-url=\"http:\/\/nosolomates.es\/?page_id=9938\" data-text=\"Variaciones\"  >Tweet<\/a><\/li><li class=\"share-linkedin\"><div class=\"linkedin_button\"><script type=\"in\/share\" data-url=\"http:\/\/nosolomates.es\/?page_id=9938\" data-counter=\"right\"><\/script><\/div><\/li><li class=\"share-pinterest\"><div class=\"pinterest_button\"><a href=\"https:\/\/www.pinterest.com\/pin\/create\/button\/?url=http%3A%2F%2Fnosolomates.es%2F%3Fpage_id%3D9938&#038;media=http%3A%2F%2F0.gravatar.com%2Favatar%2Fc9ba1828908559b850337a4baa073367%3Fs%3D96%26d%3Dmm%26r%3Dg&#038;description=Variaciones\" data-pin-do=\"buttonPin\" data-pin-config=\"beside\"><img src=\"\/\/assets.pinterest.com\/images\/pidgets\/pinit_fg_en_rect_gray_20.png\" \/><\/a><\/div><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Herramienta para calcular el n\u00famero de variaciones de n elementos en grupos de k elementos. Introduce el n\u00famero en la caja y pulsa &#8220;Calcular&#8221;. Para ver los agrupamientos, pulsa &#8220;Agrupamientos&#8221;. Texto alternativo para browsers que no aceptan iframes. Explicaci\u00f3n: Las &hellip; <a href=\"http:\/\/nosolomates.es\/?page_id=9938\">Sigue leyendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-official sd-sharing\"><div class=\"sd-content\"><ul><li class=\"share-facebook\"><div class=\"fb-share-button\" data-href=\"http:\/\/nosolomates.es\/?page_id=9938\" data-layout=\"button_count\"><\/div><\/li><li class=\"share-twitter\"><a href=\"https:\/\/twitter.com\/share\" class=\"twitter-share-button\" data-url=\"http:\/\/nosolomates.es\/?page_id=9938\" data-text=\"Variaciones\"  >Tweet<\/a><\/li><li class=\"share-linkedin\"><div class=\"linkedin_button\"><script type=\"in\/share\" data-url=\"http:\/\/nosolomates.es\/?page_id=9938\" data-counter=\"right\"><\/script><\/div><\/li><li class=\"share-pinterest\"><div class=\"pinterest_button\"><a href=\"https:\/\/www.pinterest.com\/pin\/create\/button\/?url=http%3A%2F%2Fnosolomates.es%2F%3Fpage_id%3D9938&#038;media=http%3A%2F%2F0.gravatar.com%2Favatar%2Fc9ba1828908559b850337a4baa073367%3Fs%3D96%26d%3Dmm%26r%3Dg&#038;description=Variaciones\" data-pin-do=\"buttonPin\" data-pin-config=\"beside\"><img src=\"\/\/assets.pinterest.com\/images\/pidgets\/pinit_fg_en_rect_gray_20.png\" \/><\/a><\/div><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"author":1,"featured_media":0,"parent":623,"menu_order":14,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"jetpack_shortlink":"https:\/\/wp.me\/P9BfV-2Ai","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/9938"}],"collection":[{"href":"http:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/nosolomates.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9938"}],"version-history":[{"count":11,"href":"http:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/9938\/revisions"}],"predecessor-version":[{"id":9949,"href":"http:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/9938\/revisions\/9949"}],"up":[{"embeddable":true,"href":"http:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/623"}],"wp:attachment":[{"href":"http:\/\/nosolomates.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}