{"id":34066,"date":"2021-03-26T00:00:29","date_gmt":"2021-03-26T00:00:29","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34066"},"modified":"2025-08-15T08:56:00","modified_gmt":"2025-08-15T08:56:00","slug":"technicae-computandi-permutatio-variatio-et-combinatio","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/technicae-computandi-permutatio-variatio-et-combinatio\/","title":{"rendered":"Technicae Computandi: Permutatio, Variatio et Combinatio"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Technicae Computandi: Permutatio, Variatio et Combinatio<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>Summarium<\/strong><br \/><em>In studio probabilitatum, technicae computandi sunt instrumenta fundamentalia ad mensurandam cardinalitatem spatii exemplaris et eventus metiendi. Hoc sensu, technicae combinationis, variationis et permutationis sunt usitatissimae propter facilitatem usus et applicationem in experimentis cum eventibus aequiprobabilibus. Per mensuram probabilitatis ut limitem frequentiarum relativarum, probabilitas eventus statuitur ut quotiens cardinalitatum. Quam ob rem, calculus probabilitatum ad calculum cardinalitatis spatii exemplaris et eventus metiendi reducitur. Hoc sensu, obtentio technicarum computandi per experimenta cum eventibus aequiprobabilibus est momenti ad studium probabilitatum. Per definitionem variationum, combinationum et permutationum, magnitudo collectionum efficaciter et accurate metiri potest. In hac lectione plura experimenta cum eventibus aequiprobabilibus proposita exhibebuntur et eorum spatia exemplaria examinabuntur ad technicas computandi introducendas. His instrumentis, magnitudo multarum collectionum variarum metiri poterit et probabilitates eventuum in experimentis cum eventibus aequiprobabilibus calculabuntur.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>PROPOSITA DISCENDI:<\/strong><br \/>\nPeracta hac lectione discipulus poterit:\n<\/p>\n<ol>\n<strong>Meminisse<\/strong> formulam casuum favorabilium super casus possibiles tamquam modum ad probabilitatem eventus computandam.<br \/>\n<strong>Intelligere<\/strong> notiones permutationis, variationis et combinationis earumque usum in calculo probabilitatum.<br \/>\n<strong>Analyzare<\/strong> et explicare relationem inter magnitudinem spatii exemplaris et probabilitatem eventus in experimento cum eventibus aequiprobabilibus.<br \/>\n<strong>Identificare<\/strong> casus in vita cotidiana in quibus technicae computandi combinationis, variationis et permutationis adhiberi possunt, ut in ludis aleae et in quaestionibus ordinandi.\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX CONTENTORUM<\/strong><br \/>\n<a href=\"#1\"><strong>TECHNICAE COMPUTANDI ET PROBABILITATES<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>OBTENTIO TECHNICARUM COMPUTANDI<\/strong><\/a><br \/>\n<a href=\"#3\">EXPERIMENTUM 1 (AORM): AGERE \u2013 NOTARE ORDINE \u2013 RESECARE, ITERARE M VICIBUS<\/a><br \/>\n<a href=\"#4\">EXPERIMENTUM 2 (AOK): AGERE \u2013 NOTARE ORDINE, ITERARE K VICIBUS<\/a><br \/>\n<a href=\"#5\">EXPERIMENTUM 3 (ADK): AGERE \u2013 NOTARE SINE ORDINE, ITERARE K VICIBUS<\/a><\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/72LBcZP7Fv4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Technicae computandi et probabilitates<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=7s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Combinatio, Variatio et Permutatio sunt technicae computandi maxime usitatae in studio probabilitatum<\/span><\/strong><\/a> propter commoditates quas introducunt in studio experimentorum cum eventibus aequiprobabilibus. Unum ex exemplis iconicis horum experimentorum provenit ex ludis aleae. Haec plerumque sunt processus non deterministici super spatium exemplare <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega = \\{\\omega_1, \\omega_2, \\cdots, \\omega_N\\}<\/span>. Haec experimenta communem qualitatem habent quod omnes eventus formae <span class=\"katex-eq\" data-katex-display=\"false\">\\{\\omega_i\\}\\in\\mathcal{A}_\\Omega<\/span>, cum <span class=\"katex-eq\" data-katex-display=\"false\">i\\in\\{1,2,\\cdots, n\\}<\/span>, eandem probabilitatem habent eveniendi.<\/p>\n<p style=\"text-align: justify;\">Ex <strong><a href=\"https:\/\/toposuranos.com\/el-espacio-de-probabilidades-medida-de-probabilidad\/\" target=\"_blank\" rel=\"noopener\">mensura probabilitatis ut limite frequentiarum relativarum<\/a><\/strong> possumus statuere probabilitatem eventus ut quotiens cardinalitatum. Ut iam vidimus, hoc fit per relationem:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(E) = \\displaystyle \\lim_{N\\to\\infty}g_N(E) = \\lim_{N\\to\\infty}\\frac{f_N(E)}{N}= \\frac{\\# E}{\\# \\Omega}<\/span>\n<p style=\"text-align: justify;\">Hic symbolum \u00ab#\u00bb refertur ad cardinalitatem collectionis. Hoc est quod notum est ut <strong>formula casuum favorabilium super casus possibiles.<\/strong><\/p>\n<p style=\"text-align: justify;\">In his condicionibus, calculus probabilitatum ad calculum cardinalitatis spatii exemplaris et eventus metiendi reducitur. Quam ob rem valde utile erit prius recensere quasdam <strong>technicas computandi.<\/strong><\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Obtentio Technicarum Computandi<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=260s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>Ad introducendas combinationes, variationes et permutationes,<\/strong><\/span><\/a> concipiemus quaedam experimenta cum eventibus aequiprobabilibus, et ex his faciemus consequentias quae ad has technicas computandi ducunt.<\/p>\n<p style=\"text-align: justify;\">Ponamus nos habere \u00abmachinam aleatoriam perfectam\u00bb, quae constat ex cista nigra, memoria, plectro actionis et altero plectro resectionis. Machina has proprietates habet:<\/p>\n<ol>\n<li style=\"text-align: justify;\">Machina unam tantum habet configurationem personalizabilem: cardinalitatem sui spatii exemplaris <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N = \\{\\omega_1,\\cdots,\\omega_N\\}<\/span><\/li>\n<li style=\"text-align: justify;\">Premendo plectrum actionis, ostendet in schemate unum ex elementis <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N<\/span><\/li>\n<li style=\"text-align: justify;\">Cum eventus ostenditur, is in memoria reponitur, et dum ibi manet non iterum ostendetur premendo plectrum actionis.<\/li>\n<li style=\"text-align: justify;\">Si machina iam omnes eventus possibiles ostendit, se congelabit et nihil ostendet.<\/li>\n<li style=\"text-align: justify;\">Plectrum resectionis delet memoriam et id quod in schemate ostenditur.<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">Hac machina concipiemus quaedam experimenta et eorum spatia exemplaria examinabimus.<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>Experimentum 1 (AORm): Agere &#8211; Notare ordine &#8211; ReseCare, iterare m vicibus<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=406s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Machina configuratur cum<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega = N<\/span> et repetuntur <span class=\"katex-eq\" data-katex-display=\"false\">m\\leq N<\/span> vicibus haec series graduum:<\/p>\n<ol>\n<li style=\"text-align: justify;\">Premere plectrum actionis<\/li>\n<li style=\"text-align: justify;\">Notare eventum in indice ordinato<\/li>\n<li style=\"text-align: justify;\">Resecare<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">Cum perfecerimus, obtinebimus indicem ordinatum cum <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> elementis <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N = \\{\\omega_1,\\cdots,\\omega_N\\}<\/span>. Hic index potest interpretari ut m-tupla <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N<\/span>. Aliis verbis, spatium exemplare huius experimenti <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{AORm}<\/span> erit huius formae<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{AORm}=\\Omega_N \\times \\cdots \\times \\Omega_N = \\Omega_N^m<\/span>\n<p style=\"text-align: justify;\">Itaque habebitur <span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega_{AORm}=\\#\\Omega_N^m = N^m<\/span>.<\/p>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>Experimentum 2 (AOk): Agere &#8211; Notare ordine, iterare k vicibus<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=542s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Iterum machinam configuramus cum<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega = N<\/span> et repetitur <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> vicibus (<span class=\"katex-eq\" data-katex-display=\"false\">k\\leq N<\/span>) haec series graduum:<\/p>\n<ol>\n<li style=\"text-align: justify;\">Premere plectrum actionis.<\/li>\n<li style=\"text-align: justify;\">Notare eventum in indice ordinato.<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">Cum perfecerimus, habebimus indicem ordinatum <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> elementorum <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N = \\{\\omega_1,\\cdots,\\omega_N\\}<\/span>, sed nullum elementum iterabitur cum aliquo ex iis quae praecesserunt.<\/p>\n<p style=\"text-align: justify;\">Cum machina, principio, nullum eventum possibile alteri praeferat (quia perfecte aleatoria est), licet sine iactura generalitatis assumere quod, cum primum actum est, eventus <span class=\"katex-eq\" data-katex-display=\"false\">\\{\\omega_1\\}<\/span> evenit, ita spatium exemplare actionis sequentis erit <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N\\setminus\\{\\omega_1\\}<\/span>. Similiter, licet assumere sine iactura generalitatis quod, cum secundo actum est, evenit eventus <span class=\"katex-eq\" data-katex-display=\"false\">\\{\\omega_2\\}<\/span>; ergo spatium exemplare actionis sequentis erit huius formae <span class=\"katex-eq\" data-katex-display=\"false\">(\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}<\/span>. Si hoc modo procedamus, cum ad actionem k-essimam pervenerimus, haec habebit spatium exemplare huius formae<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\cdots(\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}\\cdots)\\setminus\\{\\omega_{k-1}\\}<\/span>\n<p style=\"text-align: justify;\">Ita spatium exemplare eventuum possibilium huius experimenti erit huius formae<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{AOk}= \\Omega \\times (\\Omega_N\\setminus\\{\\omega_1\\}) \\times ((\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}) \\times \\cdots \\times ((\\cdots(\\Omega_N\\setminus\\{\\omega_1\\})\\setminus\\{\\omega_2\\}\\cdots)\\setminus\\{\\omega_{k-1}\\}) <\/span>\n<p style=\"text-align: justify;\">Quare si cardinalitatem huius collectionis computemus, obtinebimus<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega_{AOk}= N \\cdot (N-1) \\cdot (N-2) \\cdots [N-(k-1)]=\\displaystyle \\frac{N!}{(N-k)!}<\/span>\n<p style=\"text-align: justify;\">Ex hoc effectu nascitur haec definitio:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; color: #800000; background-color: #dddddd;\"><strong>DEFINITIO<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; background-color: #ffffff;\">Definimus <strong>numerum variationum<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> elementorum in coetibus <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> (cum <span class=\"katex-eq\" data-katex-display=\"false\">N\\leq k<\/span>) ut numerum datum per:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(N)_k = \\displaystyle \\frac{N!}{(N-k)!}<\/span>\n<p>Ex hoc, et ex facto quod <span class=\"katex-eq\" data-katex-display=\"false\">0! =1<\/span>, computatur <strong>numerus permutationum<\/strong> inter <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> elementa per<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(N)_N = N!<\/span>.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>Experimentum 3 (ADk): Agere &#8211; Notare sine ordine, iterare k vicibus<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=72LBcZP7Fv4&amp;t=1204s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Hoc experimentum prorsus idem est ac prius,<\/span><\/strong><\/a> nisi quod nunc non registratur ordo quo elementa <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N<\/span> apparent. Id est, quae essent duae k-tuplae cum eisdem elementis sed in diverso ordine, nunc pro eadem re habentur. Ita, cum unaquaeque k-tupla ex experimento AOk obtenta scribi possit <span class=\"katex-eq\" data-katex-display=\"false\">(k)_k=k!<\/span> modis diversis, habebitur cardinalitas spatii exemplaris huius experimenti huius formae<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\#\\Omega_{ADk} = \\displaystyle \\frac{\\#\\Omega_{AOk}}{(k)_k} = \\frac{(N)_k}{k!} = \\frac{N!}{k!(N-k)!} <\/span>\n<p style=\"text-align: justify;\">Ex hoc constitui potest haec definitio:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; color: #800000; background-color: #dddddd;\"><strong>DEFINITIO<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; background-color: #ffffff;\">Definimus <strong>numerum combinationum<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> elementorum in coetibus <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> (cum <span class=\"katex-eq\" data-katex-display=\"false\">k\\leq N<\/span>) per numerum datum<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{N}\\choose{k}}= \\frac{N!}{k!(N-k)!} <\/span>\n<p>Hoc repraesentat numerum subcollectionum possibilium quae formari possunt cum k elementis ex alio coetu cum N elementis.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Technicis computandi permutationis, variationis et combinationis nunc magnitudinem multarum collectionum variarum metiri poterimus.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Technicae Computandi: Permutatio, Variatio et Combinatio SummariumIn studio probabilitatum, technicae computandi sunt instrumenta fundamentalia ad mensurandam cardinalitatem spatii exemplaris et eventus metiendi. Hoc sensu, technicae combinationis, variationis et permutationis sunt usitatissimae propter facilitatem usus et applicationem in experimentis cum eventibus aequiprobabilibus. Per mensuram probabilitatis ut limitem frequentiarum relativarum, probabilitas eventus statuitur ut quotiens cardinalitatum. Quam [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26383,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1298,1364],"tags":[],"class_list":["post-34066","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematica","category-probabilitates-et-statistica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Technicae Computandi: Permutatio, Variatio et Combinatio - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Disce quomodo adhibere technicas computandi maxime usitatas in probabilitatibus: permutationem, variationem et combinationem cum exemplis practicis.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/la\/technicae-computandi-permutatio-variatio-et-combinatio\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Technicae Computandi: Permutatio, Variatio et Combinatio\" \/>\n<meta property=\"og:description\" content=\"Disce quomodo adhibere technicas computandi maxime usitatas in probabilitatibus: permutationem, variationem et combinationem cum exemplis practicis.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/la\/technicae-computandi-permutatio-variatio-et-combinatio\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-26T00:00:29+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-08-15T08:56:00+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/04\/conteotechniques.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Technicae Computandi: Permutatio, Variatio et Combinatio\" \/>\n<meta name=\"twitter:description\" content=\"Disce quomodo adhibere technicas computandi maxime usitatas in probabilitatibus: permutationem, variationem et combinationem cum exemplis practicis.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/04\/conteotechniques.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/technicae-computandi-permutatio-variatio-et-combinatio\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/technicae-computandi-permutatio-variatio-et-combinatio\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Technicae Computandi: Permutatio, Variatio et Combinatio\",\"datePublished\":\"2021-03-26T00:00:29+00:00\",\"dateModified\":\"2025-08-15T08:56:00+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/technicae-computandi-permutatio-variatio-et-combinatio\\\/\"},\"wordCount\":1092,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/technicae-computandi-permutatio-variatio-et-combinatio\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/04\\\/conteotechniques.jpg\",\"articleSection\":[\"Mathematica\",\"Probabilitates et Statistica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/technicae-computandi-permutatio-variatio-et-combinatio\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/technicae-computandi-permutatio-variatio-et-combinatio\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/technicae-computandi-permutatio-variatio-et-combinatio\\\/\",\"name\":\"Technicae Computandi: Permutatio, Variatio et Combinatio - 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