{"id":1207,"date":"2026-05-06T11:15:19","date_gmt":"2026-05-06T09:15:19","guid":{"rendered":"https:\/\/clases.jesussoto.es\/?p=1207"},"modified":"2026-04-02T18:44:38","modified_gmt":"2026-04-02T16:44:38","slug":"mad-combinaciones-con-maxima","status":"publish","type":"post","link":"https:\/\/clases.jesussoto.es\/?p=1207","title":{"rendered":"MAD: Combinaciones con maxima"},"content":{"rendered":"<p>Sabemos que \\[\\binom{n}{k} = \\binom{n-1}{k-1} + \\binom{n-1}{k}\\]<\/p>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Crear una funci\u00f3n recursiva que nos permita calcular \\[\\binom{n}{k}\\]\n<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv1ed1() {\n  var htmlShow1ed1 = document.getElementById(\"html-show1ed1\");\n  if (htmlShow1ed1.style.display === \"none\") {\n    htmlShow1ed1.style.display = \"block\";\n  } else {\n    htmlShow1ed1.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1ed1()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1ed1\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i1)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_comment\">\/* Definici\u00f3n de la funci\u00f3n para un n\u00famero binomial recursiva *\/<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\">if <\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">0<\/span><span class=\"code_function\"> or <\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">n<\/span><span class=\"code_function\"> then <\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\"> else <\/span><span class=\"code_function\">if <\/span><span class=\"code_variable\">k<\/span><span class=\"code_endofline\">&gt;<\/span><span class=\"code_variable\">n<\/span><span class=\"code_function\"> or <\/span><span class=\"code_variable\">k<\/span><span class=\"code_endofline\">&lt;<\/span><span class=\"code_number\">0<\/span><span class=\"code_function\"> then <\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\"> else <\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">10<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }120\\]<\/p>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Utlizando $$PR_{n}^{n_1, n_2, \\dots, n_r} = \\binom{n}{n_1} \\cdot \\binom{n &#8211; n_1}{n_2} \\cdot \\binom{n &#8211; n_1 &#8211; n_2}{n_3} \\cdots \\binom{n_r}{n_r}$$ crear una funci\u00f3n que nos calcule $PR_{n}^{n_1, n_2, \\dots, n_r}$\n<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv1ed12() {\n  var htmlShow1ed12 = document.getElementById(\"html-show1ed12\");\n  if (htmlShow1ed12.style.display === \"none\") {\n    htmlShow1ed12.style.display = \"block\";\n  } else {\n    htmlShow1ed12.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1ed12()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1ed12\" style=\"display: none;\">\nUtilicemos la funci\u00f3n creada antes para calcular un n\u00famero combinatorio.<br \/>\n <!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">PR<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">lista_k<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_function\">block<\/span><span class=\"code_operator\">(<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_operator\">[<\/span><span class=\"code_variable\">resultado<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n_restante<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">n<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">r<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_comment\">\/* r es el n\u00famero de grupos en la lista *\/<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_variable\">r<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">length<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">lista_k<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_comment\">\/* Recorremos la lista usando un contador i *\/<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\">for <\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">1<\/span><span class=\"code_function\"> thru <\/span><span class=\"code_variable\">r<\/span><span class=\"code_function\"> do <\/span><span class=\"code_operator\">(<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"code_comment\">\/* Multiplicamos por el binomio actual *\/<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"code_variable\">resultado<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">resultado<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n_restante<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">lista_k<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"code_comment\">\/* Actualizamos los huecos que quedan disponibles *\/<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"code_variable\">n_restante<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">n_restante<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_variable\">lista_k<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\">return<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">resultado<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Utilizando la funci\u00f3n recursiva creada para los n\u00fameros binomiales, calcula la suma de los coeficientes impares del desarrollo de \\((x+y)^{21}\\). Es decir, \\[\\sum_{i=0}^{\\left\\lfloor \\frac{21}{2}\\right\\rfloor}\\binom{21}{2i+1}\\]\n<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv1ed123() {\n  var htmlShow1ed123 = document.getElementById(\"html-show1ed123\");\n  if (htmlShow1ed123.style.display === \"none\") {\n    htmlShow1ed123.style.display = \"block\";\n  } else {\n    htmlShow1ed123.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1ed123()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1ed123\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i1)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_comment\">\/* Definici\u00f3n de la funci\u00f3n para un n\u00famero binomial recursiva *\/<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\">if <\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">0<\/span><span class=\"code_function\"> or <\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">n<\/span><span class=\"code_function\"> then <\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\"> else <\/span><span class=\"code_function\">if <\/span><span class=\"code_variable\">k<\/span><span class=\"code_endofline\">&gt;<\/span><span class=\"code_variable\">n<\/span><span class=\"code_function\"> or <\/span><span class=\"code_variable\">k<\/span><span class=\"code_endofline\">&lt;<\/span><span class=\"code_number\">0<\/span><span class=\"code_function\"> then <\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\"> else <\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">k<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i4)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">n<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">for <\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">0<\/span><span class=\"code_function\"> thru <\/span><span class=\"code_function\">floor<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">21<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_function\"> do <\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">binomio<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">21<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">+<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">n<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }1048576\\]<\/p>\n<\/div>\n<hr \/>\n<p>Las combinaciones con repetici\u00f3n admiten una f\u00f3rmula recursiva: para todos enteros positivos \\(0&lt;n\\) y \\(0\\leq m\\), es \\[CR_{n,m}=CR_{n-1,m}+CR_{n,m-1}, \\] siendo \\(CR_{1,m}=1\\) y \\(CR_{n,1}=n\\). As\u00ed \\[\\left(\\!\\!\\!{n \\choose m}\\!\\!\\!\\right)=\\left(\\!\\!\\!{n-1 \\choose m}\\!\\!\\!\\right)+\\left(\\!\\!\\!{n \\choose m-1}\\!\\!\\!\\right)\\]<\/p>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Utilizando el procedimiento recursivo anterior, crea una funci\u00f3n que nos permita calcular cu\u00e1nto es \\(\\left(\\!\\!{5 \\choose 3}\\!\\!\\right)\\)<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv1e02() {\n  var htmlShow1e02 = document.getElementById(\"html-show1e02\");\n  if (htmlShow1e02.style.display === \"none\") {\n    htmlShow1e02.style.display = \"block\";\n  } else {\n    htmlShow1e02.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1e02()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1e02\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i1)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_comment\">\/* Funci\u00f3n recursiva para Combinaciones con Repetici\u00f3n *\/<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">CR<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">m<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\">if <\/span><span class=\"code_variable\">m<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">0<\/span><span class=\"code_function\"> then <\/span><span class=\"code_number\">1<\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"code_comment\">\/* Caso base: ya hemos elegido todos los elementos *\/<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\">else <\/span><span class=\"code_function\">if <\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">0<\/span><span class=\"code_function\"> then <\/span><span class=\"code_number\">0<\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"code_comment\">\/* Caso base: no quedan tipos de elementos para elegir *\/<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_function\">else <\/span><span class=\"code_function\">CR<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">m<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">CR<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">m<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">CR<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }35\\]<\/p>\n<\/div>\n<hr \/>\n<h2>Construcci\u00f3n de las combinaciones<\/h2>\n<p>Hasta ahora hemos construido funciones que nos determinan el valor de las variaciones, permutaciones y combinaciones.<\/p>\n<p>Supongamos que deseamos construir todos los posibles subconjuntos de dos elementos de un conjunto finito; es decir, las combinaciones de \\(n\\) elementos tomados de dos en dos. La forma m\u00e1s sencilla ser\u00eda mediante<\/p>\n<p>\\[\\begin{array}{l} \\mathrm{Sea }\\,A=\\{x_1,x_2,\\ldots,x_n\\};\\\\ \\mathbf{for}\\, i=1\\, \\mathbf{thru}\\, n-1 \\,\\mathbf{do}(\\\\ \\qquad \\mathbf{for }\\,  j=i+1\\, \\mathbf{thru}\\, n \\,\\mathbf{do}( \\\\ \\qquad\\qquad\\{x_i,x_j\\}\\\\ \\qquad )\\\\ )\\end{array} \\]<\/p>\n<p>\u00bfC\u00f3mo podr\u00edamos construir las variaciones? \u00bfY las permutaciones?<\/p>\n<hr \/>\n<table id=\"yzpi\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"3\" bgcolor=\"#999999\">\n<tbody>\n<tr>\n<td width=\"100%\"><strong>Ejercicio:<\/strong> En una reuni\u00f3n de 10 personas debe nombrarse una comisi\u00f3n formada por tres de ellas. \u00bfCu\u00e1ntas comisiones distintas podr\u00edan nombrarse?<\/td>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"100%\" >\n<div id=\"menu-a\" >\n<ul>\n<li>160<\/li>\n<li>120<\/li>\n<li>80<\/li>\n<\/ul>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><script>\nfunction showHtmlDiv() {\n  var htmlShow = document.getElementById(\"html-show\");\n  if (htmlShow.style.display === \"none\") {\n    htmlShow.style.display = \"block\";\n  } else {\n    htmlShow.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show\" style=\"display: none;\">\n<p id=\"htmlContent\" class=\"text-html\"><strong>B.)<\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Sabemos que \\[\\binom{n}{k} = \\binom{n-1}{k-1} + \\binom{n-1}{k}\\] Ejercicio: Crear una funci\u00f3n recursiva que nos permita calcular \\[\\binom{n}{k}\\] Soluci\u00f3n: (%i1) \/* Definici\u00f3n de la funci\u00f3n para un n\u00famero binomial recursiva *\/binomio(n,k):= \u00a0\u00a0 if&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[9],"class_list":["post-1207","post","type-post","status-publish","format-standard","hentry","category-matematica-discreta","tag-practicas-mad"],"_links":{"self":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1207","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1207"}],"version-history":[{"count":11,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1207\/revisions"}],"predecessor-version":[{"id":1216,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1207\/revisions\/1216"}],"wp:attachment":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1207"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1207"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}