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Permutations

Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders.

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Permutations -

Tag(s) : Combinatorics, Mathematics

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# Permutations

## Counting Permutations/Anagrams

Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders.

### How to generate permutations?

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 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. Count the number of permutations of these repeated items.

Example: DCODE 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.