--- title: Permutations without Repetition - Explaining the n! Formula description: Permutations without repetition count orders of distinct objects. The count is n factorial. url: https://astra-ai.co/videos/combinatorics/permutations/permutations-without-repetition/ locale: en type: video-lesson keywords: - permutations without repetition - ordered arrangements - n factorial - distinct objects published: 2026-10-01T09:58:28.274Z updated: 2026-10-04T22:01:47.961Z alternates: en: https://astra-ai.co/videos/combinatorics/permutations/permutations-without-repetition/ lo: https://astra-ai.co/lo/videos/lo-dd33883f/lo-15458541/lesson-78081089/ it: https://astra-ai.co/it/videos/combinatoria/permutazioni/permutazioni-senza-ripetizione/ fr: https://astra-ai.co/fr/videos/combinatoire/permutations/permutations-sans-repetition/ de: https://astra-ai.co/de/videos/kombinatorik/permutationen/permutationen-ohne-wiederholung/ hr: https://astra-ai.co/hr/videos/kombinatorika/permutacije/permutacije-bez-ponavljanja/ sl: https://astra-ai.co/sl/videos/kombinatorika/permutacije/permutacije-brez-ponavljanja/ pt: https://astra-ai.co/pt/videos/combinatoria/permutacoes/permutacoes-sem-repeticao/ nl: https://astra-ai.co/nl/videos/combinatoriek/permutaties/permutaties-zonder-herhaling/ da: https://astra-ai.co/da/videos/kombinatorik/permutationer/permutationer-uden-gentagelse/ el: https://astra-ai.co/el/videos/syndyastiki/metatheseis/permutations-without-repetition/ cs: https://astra-ai.co/cs/videos/kombinatorika/permutace/permutace-bez-opakovani/ bg: https://astra-ai.co/bg/videos/kombinatorika/permutatsii/permutatsii-bez-povtorenie/ fi: https://astra-ai.co/fi/videos/kombinatorikka/permutaatiot/permutaatiot-ilman-toistoa/ no: https://astra-ai.co/no/videos/kombinatorikk/permutasjoner/permutasjoner-uten-repetisjon/ id: https://astra-ai.co/id/videos/kombinatorika/permutasi/permutasi-tanpa-pengulangan/ hu: https://astra-ai.co/hu/videos/kombinatorika/permutaciok/ismetles-nelkuli-permutaciok/ ro: https://astra-ai.co/ro/videos/combinatorica/permutari/lectie-video-78081089/ sv: https://astra-ai.co/sv/videos/kombinatorik/permutationer/permutationer-utan-repetition/ lv: https://astra-ai.co/lv/videos/kombinatorika/permutacijas/stunda-78081089/ lt: https://astra-ai.co/lt/videos/kombinatorika/perrikiavimai/pamoka-78081089/ uk: https://astra-ai.co/uk/videos/uk-topic-05/uk-chapter-04/uk-lesson-78081089/ vi: https://astra-ai.co/vi/videos/vi-topic-05/vi-chapter-04/hoan-vi-khong-lap/ sk: https://astra-ai.co/sk/videos/kombinatorika/kapitola-050/lekcia-042/ sr: https://astra-ai.co/sr/videos/kombinatorika/poglavlje-050/lekcija-042/ th: https://astra-ai.co/th/videos/combinatorics/bot-04-riang-sap-plian/botrian-042/ tr: https://astra-ai.co/tr/videos/kombinatorik/bolum-050/ders-042/ ms: https://astra-ai.co/ms/videos/combinatorics/bab-04-matematik-asas/pelajaran-042/ es-CL: https://astra-ai.co/es-CL/videos/combinatoria/capitulo-50/leccion-de-matematicas-42/ my: https://astra-ai.co/my/videos/my-dd33883f/my-15458541/lesson-78081089/ zh-TW: https://astra-ai.co/zh-TW/videos/combinatorics/chapter-15458541/lesson-78081089/ km: https://astra-ai.co/km/videos/combinatorics/chapter-15458541/lesson-78081089/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-005/shuxue-zhang-004/shuxue-kecheng-042/ br: https://astra-ai.co/br/videos/combinatoria/capitulo-matematica-004/video-matematica-042/ es-AR: https://astra-ai.co/es-AR/videos/combinatoria/capitulo-50/leccion-42/ en-PH: https://astra-ai.co/en-PH/videos/combinatorics/chapter-15458541/lesson-78081089/ es-PE: https://astra-ai.co/es-PE/videos/combinatoria/capitulo-video-15458541/leccion-de-video-78081089/ en-IN: https://astra-ai.co/en-IN/videos/combinatorics/chapter-15458541/permutations-without-repetition/ ms-BN: https://astra-ai.co/ms-BN/videos/kombinatorik/bab-15458541/pelajaran-78081089/ mx: https://astra-ai.co/mx/videos/combinatoria/capitulo-50/leccion-42/ pt-TL: https://astra-ai.co/pt-TL/videos/combinatoria/capitulo-de-video-050/licao-de-video-042/ et: https://astra-ai.co/et/videos/kombinatoorika/permutatsioonid/permutatsioonid-kordusteta/ ko: https://astra-ai.co/ko/videos/combinatorics-ko/50/042/ ja: https://astra-ai.co/ja/videos/combinatorics-ja/50/042/ es: https://astra-ai.co/es/videos/combinatoria/permutaciones/permutaciones-sin-repeticion/ pl: https://astra-ai.co/pl/videos/kombinatoryka/permutacje/permutacje-bez-powtorzen/ --- # Permutations without Repetition > Permutations without repetition count the orders of distinct objects. This lesson shows why the count is n factorial. ## DEFINITION AND BASICS Permutations without repetition are a fundamental concept in combinatorics that deals with arranging distinct elements in a specific order. This mathematical concept allows us to calculate the number of possible arrangements of **n** different elements, where no element appears more than once. A permutation without repetition is an **ordered set** of elements where the order of placement plays a crucial role. For a group of _n_ different elements, the number of all possible permutations is given by the formula **P(n) = n!**, where _n!_ (n-factorial) denotes the product of all positive integers from 1 to n. ## IMPORTANT CHARACTERISTICS A key aspect of permutations without repetition is that the **order of elements distinguishes one permutation from another**. This means that if you swap the places of two elements, you get a completely new permutation. This property is vital for solving problems that require a precise order, such as creating schedules or arranging competition brackets. ## PRACTICAL EXAMPLE Let's look at an example for better understanding. If we have three different books (A, B, C) and want to find out how many ways we can arrange them on a shelf, we use the formula for permutations without repetition. In this case, **n = 3**, so the number of possible permutations is: P(3) = 3! = 3 \* 2 \* 1 = **6** The possible arrangements (permutations) of the books are: **ABC, ACB, BAC, BCA, CAB, and CBA**. ## CONCLUSION Permutations without repetition are a basic but powerful mathematical tool with many applications in both theory and practice. Understanding this concept is crucial for math students and anyone involved in analyzing different types of arrangements. This concept not only solves complex problems but also promotes logical thinking and a deeper understanding of mathematical principles.