Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.

Permutations - dCode

Tag(s) : Combinatorics

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⮞ Go to: Rank of a Permutation

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Item **permutations** consist in the list of all possible arrangements and ordering of elements in any order.

__Example:__ The three letters `A,B,C` can be shuffled (anagrams) in 6 ways: `A,B,C` `B,A,C` `C,A,B` `A,C,B` `B,C,A` `C,B,A`

**Permutations** should not be confused with combinations (for which the order has no influence) or with arrangements also called partial **permutations** (k-permutations of some elements).

Counting **permutations** uses combinatorics and factorials

__Example:__ For $ n $ items, the number of **permutations** is equal to $ n! $ (factorial of $ n $)

Having a repeated item involves a division of the number of **permutations** by the number of **permutations** of these repeated items.

__Example:__ `DCODE` 5 letters have $ 5! = 120 $ **permutations** but contain the letter `D` twice (these $ 2 $ letters `D` have $ 2! $ **permutations**), so divide the total number of **permutations** $ 5! $ by $ 2! $: $ 5!/2!=60 $ distinct **permutations**.

**Permutations** make exponential values which need huge computing servers with huge memory cells, so the generation are not free.

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- Permutations Generator
- Permutations from List Generator
- Permutations/Anagrams Calculator
- Rank/Ordinal Number of a Permutation
- Random Permutation
- What is a permutation? (Definition)
- How to generate permutations?
- How to count permutations?
- How to count distinct permutations?
- How to remove the limit when computing permutations?

permutation,arrangement,counting,anagram,combinatorics

Source : https://www.dcode.fr/permutations-generator

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