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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.

Permutation Generator

Permutations/Anagrams Calculator

Answers to Questions

What is a permutation? (Definition)

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

Example: A,B,C can be shuffled in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

For partial permutations (A,B among A,B,C) see arrangements.

How to generate permutations?

The best known method is the Heap algorithm.

Step 1 - for each item, fix it at the beginning

Step 2 - repeat step 1 with the rest

Permutations can thus be represented as a tree of permutations: <b>permutation</b>-tree

How to count permutations?

Counting permutations uses combinatorics and factorials

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

How to count distinct permutations?

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.

How to remove the limit when computing permutations?

Permutations makes exponential values witch needs huge computing servers with huge memory cells, so the generation must be paid.

Source code

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