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Permutations

The permutation is an important operation in combinatorics and in other areas of mathematics. To permute a list is to rearrange its elements. To count the permutations of a list is to count the number of unique rearrangements of the list. Wolfram|Alpha is useful for counting, generating and doing algebra with permutations.

Algebra of Permutations

Perform calculations using permutations and analyze their properties.

Describe a permutation:

Do algebra with permutations:

Compute properties of a permutation:

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Random Permutations

Generate random permutations of a specified number of elements.

Generate a random permutation:

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Permutations of a Set

Permute different types of data, such as sets with no repeat elements and lists that allow repetition.

Compute permutations of a set:

Compute distinct permutations of a list:

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Counting Permutations

Count how many rearrangements of a set or list are unique. Use different list sizes and permutation sizes.

Count permutations:

Specify a permutation size:

Count derangements:

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