{"id":24,"date":"2025-07-21T21:16:57","date_gmt":"2025-07-21T19:16:57","guid":{"rendered":"https:\/\/xn--szmolgp-iwa0f0e.hu\/?page_id=24"},"modified":"2025-07-21T21:16:57","modified_gmt":"2025-07-21T19:16:57","slug":"kalkulator-permutacji-obliczenia-permutacji-i-operacje-kombinatoryczne","status":"publish","type":"page","link":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\/","title":{"rendered":"Kalkulator Permutacji \u2013 Obliczenia Permutacji i Operacje Kombinatoryczne"},"content":{"rendered":"<h1 class=\"wp-block-heading has-text-align-center\" style=\"margin-bottom:2rem\">Kalkulator Permutacji \u2013 Obliczenia Permutacji i Operacje Kombinatoryczne<\/h1>\n<p class=\"has-text-align-center\" style=\"margin-bottom:3rem\">Profesjonalny kalkulator permutacji do oblicze\u0144 permutacji, problem\u00f3w z kolejno\u015bci\u0105 i operacji kombinatorycznych. Idealny wyb\u00f3r dla student\u00f3w, matematyk\u00f3w i statystyk\u00f3w.<\/p>\n<div class=\"permutacio-kalkulator-container\" data-theme=\"light\" style=\"--calculator-width: 100%; --calculator-height: auto;\">\n<div class=\"calculator\">\n<h2>Kalkulator Permutacji<\/h2>\n<p class=\"calculator-description\">Obliczenia permutacji, problemy z kolejno\u015bci\u0105 i operacje kombinatoryczne<\/p>\n<div class=\"input-section\">\n<div class=\"calculation-type\">\n<h3>Typ oblicze\u0144<\/h3>\n<p>                <select id=\"permutacioType\" class=\"form-control\"><option value=\"simple\">Prosta permutacja (n!)<\/option><option value=\"partial\">Cz\u0119\u015bciowa permutacja (nPr)<\/option><option value=\"repetition\">Permutacja z powt\u00f3rzeniami<\/option><option value=\"circular\">Permutacja cykliczna<\/option><\/select>\n            <\/div>\n<div class=\"input-group\">\n                <label for=\"permutacioN\">n (liczba element\u00f3w):<\/label><br \/>\n                <input type=\"number\" id=\"permutacioN\" class=\"form-control\" min=\"1\" max=\"100\" placeholder=\"Na przyk\u0142ad: 5\">\n            <\/div>\n<div class=\"input-group\" id=\"permutacioRGroup\" style=\"display: none;\">\n                <label for=\"permutacioR\">r (liczba wybranych element\u00f3w):<\/label><br \/>\n                <input type=\"number\" id=\"permutacioR\" class=\"form-control\" min=\"1\" max=\"100\" placeholder=\"Na przyk\u0142ad: 3\">\n            <\/div>\n<p>            <button type=\"button\" id=\"permutacioCalculate\" class=\"btn btn-primary\">Obliczenie<\/button><br \/>\n            <button type=\"button\" id=\"permutacioReset\" class=\"btn btn-secondary\">Kasowanie<\/button>\n        <\/div>\n<div class=\"result-section\" id=\"permutacioResult\" style=\"display: none;\">\n<h3>Wynik<\/h3>\n<div class=\"result-display\">\n<div class=\"result-item\">\n                    <span class=\"result-label\">Liczba permutacji:<\/span><br \/>\n                    <span class=\"result-value\" id=\"permutacioResultValue\">\u2013<\/span>\n                <\/div>\n<div class=\"result-item\">\n                    <span class=\"result-label\">Wz\u00f3r:<\/span><br \/>\n                    <span class=\"result-formula\" id=\"permutacioFormula\">\u2013<\/span>\n                <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"info-section\">\n<h3>Informacje<\/h3>\n<ul>\n<li><strong>Prosta permutacja:<\/strong> Liczba uporz\u0105dkowa\u0144 n r\u00f3\u017cnych element\u00f3w<\/li>\n<li><strong>Cz\u0119\u015bciowa permutacja:<\/strong> Wyb\u00f3r r element\u00f3w z n z uwzgl\u0119dnieniem kolejno\u015bci<\/li>\n<li><strong>Permutacja cykliczna:<\/strong> permutacje element\u00f3w u\u0142o\u017conych w okr\u0119gu<\/li>\n<\/ul><\/div>\n<\/p><\/div>\n<\/div>\n<p><script>\ndocument.addEventListener('DOMContentLoaded', function() {\n    const permutacioType = document.getElementById('permutacioType');\n    const permutacioN = document.getElementById('permutacioN');\n    const permutacioR = document.getElementById('permutacioR');\n    const permutacioRGroup = document.getElementById('permutacioRGroup');\n    const permutacioCalculate = document.getElementById('permutacioCalculate');\n    const permutacioReset = document.getElementById('permutacioReset');\n    const permutacioResult = document.getElementById('permutacioResult');\n    const permutacioResultValue = document.getElementById('permutacioResultValue');\n    const permutacioFormula = document.getElementById('permutacioFormula');<\/p>\n<p>    permutacioType.addEventListener('change', function() {\n        permutacioRGroup.style.display = permutacioType.value === 'partial' ? 'block' : 'none';\n    });<\/p>\n<p>    permutacioCalculate.addEventListener('click', function() {\n        const n = parseInt(permutacioN.value);\n        const type = permutacioType.value;<\/p>\n<p>        if (!n || n < 1) {\n            alert('K\u00e9rj\u00fck, adjon meg \u00e9rv\u00e9nyes n \u00e9rt\u00e9ket!');\n            return;\n        }\n        \n        let result, formula;\n        \n        switch(type) {\n            case 'simple':\n                result = factorial(n);\n                formula = `P(${n}) = ${n}!`;\n                break;\n            case 'partial':\n                const r = parseInt(permutacioR.value);\n                if (!r || r < 1 || r > n) {\n                    alert('K\u00e9rj\u00fck, adjon meg \u00e9rv\u00e9nyes r \u00e9rt\u00e9ket (1 \u2264 r \u2264 n)!');\n                    return;\n                }\n                result = factorial(n) \/ factorial(n - r);\n                formula = `P(${n}, ${r}) = ${n}! \/ (${n} - ${r})!`;\n                break;\n            case 'circular':\n                result = factorial(n - 1);\n                formula = `P_c(${n}) = (${n} - 1)!`;\n                break;\n        }<\/p>\n<p>        permutacioResultValue.textContent = result.toLocaleString();\n        permutacioFormula.textContent = formula;\n        permutacioResult.style.display = 'block';\n    });<\/p>\n<p>    permutacioReset.addEventListener('click', function() {\n        permutacioN.value = '';\n        permutacioR.value = '';\n        permutacioResult.style.display = 'none';\n        permutacioRGroup.style.display = 'none';\n    });<\/p>\n<p>    function factorial(n) {\n        if (n === 0 || n === 1) return 1;\n        let result = 1;\n        for (let i = 2; i <= n; i++) {\n            result *= i;\n        }\n        return result;\n    }\n});\n<\/script><\/p>","protected":false},"excerpt":{"rendered":"<p>Permut\u00e1ci\u00f3 Kalkul\u00e1tor &#8211; Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek Professzion\u00e1lis permut\u00e1ci\u00f3 kalkul\u00e1tor permut\u00e1ci\u00f3 sz\u00e1m\u00edt\u00e1sokhoz, sorrendi probl\u00e9m\u00e1khoz \u00e9s kombinatorikai m\u0171veletekhez. T\u00f6k\u00e9letes v\u00e1laszt\u00e1s di\u00e1koknak, matematikusoknak \u00e9s statisztikusoknak. Permut\u00e1ci\u00f3 Kalkul\u00e1tor Permut\u00e1ci\u00f3 sz\u00e1m\u00edt\u00e1sok, sorrendi probl\u00e9m\u00e1k \u00e9s kombinatorikai m\u0171veletek Sz\u00e1m\u00edt\u00e1s t\u00edpusa Egyszer\u0171 permut\u00e1ci\u00f3 (n!)R\u00e9szleges permut\u00e1ci\u00f3 (nPr)Permut\u00e1ci\u00f3 ism\u00e9tl\u00e9sselCiklikus permut\u00e1ci\u00f3 n (elemek sz\u00e1ma): r (kiv\u00e1lasztott elemek sz\u00e1ma): Sz\u00e1m\u00edt\u00e1s T\u00f6rl\u00e9s Eredm\u00e9ny Permut\u00e1ci\u00f3k sz\u00e1ma: &#8211; &#8230; <a title=\"Kalkulator Permutacji \u2013 Obliczenia Permutacji i Dzia\u0142ania Kombinatoryczne\" class=\"read-more\" href=\"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\/\" aria-label=\"Dowiedz si\u0119 wi\u0119cej o Permut\u00e1ci\u00f3 Kalkul\u00e1tor &#8211; Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek\">Dowiedz si\u0119 wi\u0119cej<\/a><\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-24","page","type-page","status-publish"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Permut\u00e1ci\u00f3 Kalkul\u00e1tor - Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek - Sz\u00e1mol\u00f3g\u00e9pek \u00e9s kalkul\u00e1torok gy\u0171jtem\u00e9nye<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/kalkulator-permutacji-obliczenia-permutacji-i-operacje-kombinatoryczne\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Permut\u00e1ci\u00f3 Kalkul\u00e1tor - Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek - Sz\u00e1mol\u00f3g\u00e9pek \u00e9s kalkul\u00e1torok gy\u0171jtem\u00e9nye\" \/>\n<meta property=\"og:description\" content=\"Permut\u00e1ci\u00f3 Kalkul\u00e1tor &#8211; Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek Professzion\u00e1lis permut\u00e1ci\u00f3 kalkul\u00e1tor permut\u00e1ci\u00f3 sz\u00e1m\u00edt\u00e1sokhoz, sorrendi probl\u00e9m\u00e1khoz \u00e9s kombinatorikai m\u0171veletekhez. T\u00f6k\u00e9letes v\u00e1laszt\u00e1s di\u00e1koknak, matematikusoknak \u00e9s statisztikusoknak. Permut\u00e1ci\u00f3 Kalkul\u00e1tor Permut\u00e1ci\u00f3 sz\u00e1m\u00edt\u00e1sok, sorrendi probl\u00e9m\u00e1k \u00e9s kombinatorikai m\u0171veletek Sz\u00e1m\u00edt\u00e1s t\u00edpusa Egyszer\u0171 permut\u00e1ci\u00f3 (n!)R\u00e9szleges permut\u00e1ci\u00f3 (nPr)Permut\u00e1ci\u00f3 ism\u00e9tl\u00e9sselCiklikus permut\u00e1ci\u00f3 n (elemek sz\u00e1ma): r (kiv\u00e1lasztott elemek sz\u00e1ma): Sz\u00e1m\u00edt\u00e1s T\u00f6rl\u00e9s Eredm\u00e9ny Permut\u00e1ci\u00f3k sz\u00e1ma: &#8211; ... Dowiedz si\u0119 wi\u0119cej\" \/>\n<meta property=\"og:url\" content=\"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/kalkulator-permutacji-obliczenia-permutacji-i-operacje-kombinatoryczne\/\" \/>\n<meta property=\"og:site_name\" content=\"Sz\u00e1mol\u00f3g\u00e9pek \u00e9s kalkul\u00e1torok gy\u0171jtem\u00e9nye\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\\\/\",\"url\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\\\/\",\"name\":\"Permut\u00e1ci\u00f3 Kalkul\u00e1tor - Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek - Sz\u00e1mol\u00f3g\u00e9pek \u00e9s kalkul\u00e1torok gy\u0171jtem\u00e9nye\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/#website\"},\"datePublished\":\"2025-07-21T19:16:57+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\\\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Kezd\u0151lap\",\"item\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Permut\u00e1ci\u00f3 Kalkul\u00e1tor &#8211; Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/#website\",\"url\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/\",\"name\":\"Sz\u00e1mol\u00f3g\u00e9pek \u00e9s kalkul\u00e1torok gy\u0171jtem\u00e9nye\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/xn--szmolgp-iwa0f0e.hu\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pl-PL\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Kalkulator Permutacji - Obliczenia permutacji i operacje kombinatoryczne - Kolekcja kalkulator\u00f3w i narz\u0119dzi obliczeniowych","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/kalkulator-permutacji-obliczenia-permutacji-i-operacje-kombinatoryczne\/","og_locale":"pl_PL","og_type":"article","og_title":"Permut\u00e1ci\u00f3 Kalkul\u00e1tor - Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek - Sz\u00e1mol\u00f3g\u00e9pek \u00e9s kalkul\u00e1torok gy\u0171jtem\u00e9nye","og_description":"Permut\u00e1ci\u00f3 Kalkul\u00e1tor &#8211; Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek Professzion\u00e1lis permut\u00e1ci\u00f3 kalkul\u00e1tor permut\u00e1ci\u00f3 sz\u00e1m\u00edt\u00e1sokhoz, sorrendi probl\u00e9m\u00e1khoz \u00e9s kombinatorikai m\u0171veletekhez. T\u00f6k\u00e9letes v\u00e1laszt\u00e1s di\u00e1koknak, matematikusoknak \u00e9s statisztikusoknak. Permut\u00e1ci\u00f3 Kalkul\u00e1tor Permut\u00e1ci\u00f3 sz\u00e1m\u00edt\u00e1sok, sorrendi probl\u00e9m\u00e1k \u00e9s kombinatorikai m\u0171veletek Sz\u00e1m\u00edt\u00e1s t\u00edpusa Egyszer\u0171 permut\u00e1ci\u00f3 (n!)R\u00e9szleges permut\u00e1ci\u00f3 (nPr)Permut\u00e1ci\u00f3 ism\u00e9tl\u00e9sselCiklikus permut\u00e1ci\u00f3 n (elemek sz\u00e1ma): r (kiv\u00e1lasztott elemek sz\u00e1ma): Sz\u00e1m\u00edt\u00e1s T\u00f6rl\u00e9s Eredm\u00e9ny Permut\u00e1ci\u00f3k sz\u00e1ma: &#8211; ... Dowiedz si\u0119 wi\u0119cej","og_url":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/kalkulator-permutacji-obliczenia-permutacji-i-operacje-kombinatoryczne\/","og_site_name":"Sz\u00e1mol\u00f3g\u00e9pek \u00e9s kalkul\u00e1torok gy\u0171jtem\u00e9nye","twitter_card":"summary_large_image","twitter_misc":{"Szacowany czas czytania":"1 minuta"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/xn--szmolgp-iwa0f0e.hu\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\/","url":"https:\/\/xn--szmolgp-iwa0f0e.hu\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\/","name":"Kalkulator Permutacji - Obliczenia permutacji i operacje kombinatoryczne - Kolekcja kalkulator\u00f3w i narz\u0119dzi obliczeniowych","isPartOf":{"@id":"https:\/\/xn--szmolgp-iwa0f0e.hu\/#website"},"datePublished":"2025-07-21T19:16:57+00:00","breadcrumb":{"@id":"https:\/\/xn--szmolgp-iwa0f0e.hu\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\/#breadcrumb"},"inLanguage":"pl-PL","potentialAction":[{"@type":"ReadAction","target":["https:\/\/xn--szmolgp-iwa0f0e.hu\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/xn--szmolgp-iwa0f0e.hu\/permutacio-kalkulator-permutacio-szamitasok-es-kombinatorikai-muveletek\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Kezd\u0151lap","item":"https:\/\/xn--szmolgp-iwa0f0e.hu\/"},{"@type":"ListItem","position":2,"name":"Permut\u00e1ci\u00f3 Kalkul\u00e1tor &#8211; Permut\u00e1ci\u00f3 Sz\u00e1m\u00edt\u00e1sok \u00e9s Kombinatorikai M\u0171veletek"}]},{"@type":"WebSite","@id":"https:\/\/xn--szmolgp-iwa0f0e.hu\/#website","url":"https:\/\/xn--szmolgp-iwa0f0e.hu\/","name":"Kolekcja kalkulator\u00f3w i narz\u0119dzi obliczeniowych","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/xn--szmolgp-iwa0f0e.hu\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"pl-PL"}]}},"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/wp-json\/wp\/v2\/pages\/24","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/wp-json\/wp\/v2\/comments?post=24"}],"version-history":[{"count":0,"href":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/wp-json\/wp\/v2\/pages\/24\/revisions"}],"wp:attachment":[{"href":"https:\/\/xn--szmolgp-iwa0f0e.hu\/pl\/wp-json\/wp\/v2\/media?parent=24"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}