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Mathematica > Mathematics and Algorithms > Discrete Mathematics >

Permutations

Permutations[list]
generates a list of all possible permutations of the elements in list.

Permutations[list, n]
gives all permutations containing at most n elements.

Permutations[list, {n}]
gives all permutations containing exactly n elements.

Permutations[list] is effectively equivalent to Permutations[list, {Length[list]}].

Permutations[list, {n_min, n_max}] gives permutations of between n_min and n_max elements.

Length-3 permutations of {a, b, c}:

Length-3 permutations of {a, b, c, d}:

Length-3 permutations of {a, b, c}:

Length-3 permutations of {a, b, c, d}:

Repeated elements are treated as identical:

Use any expressions as elements:

Get permutations of all lengths, shortest ones first:

Get even-length permutations, longest ones first:

The list of elements can have any head:

The number of length-n permutations of a length-n list of distinct elements is n!:

The number of length-r permutations of a length-n list of distinct elements is n!/(n-r)!:

If the input list is in the order given by Sort, so are its length-r permutations: