# 46.10 PermutationsList

`PermutationsList( mset )`

`NrPermutationsList( mset )`

`PermutationsList` returns the set of permutations of the multiset mset.

`NrPermutationsList` returns the number of permutations of the multiset mset.

A permutation is represented by a list that contains exactly the same elements as mset, but possibly in different order. If mset is a proper set there are |mset| ! (see Factorial) such permutations. Otherwise if the first elements appears k_1 times, the second element appears k_2 times and so on, the number of permutations is |mset|! / (k_1! k_2! ..), which is sometimes called multinomial coefficient.

```    gap> PermutationsList( [1,2,3] );
[ [ 1, 2, 3 ], [ 1, 3, 2 ], [ 2, 1, 3 ], [ 2, 3, 1 ], [ 3, 1, 2 ],
[ 3, 2, 1 ] ]
gap> PermutationsList( [1,1,2,2] );
[ [ 1, 1, 2, 2 ], [ 1, 2, 1, 2 ], [ 1, 2, 2, 1 ], [ 2, 1, 1, 2 ],
[ 2, 1, 2, 1 ], [ 2, 2, 1, 1 ] ]
gap> NrPermutationsList( [1,2,2,3,3,3,4,4,4,4] );
12600 ```

The function `Arrangements` (see Arrangements) is the generalization of `PermutationsList` that allows you to specify the size of the permutations. `Derangements` (see Derangements) computes permutations that have no fixpoints.

GAP 3.4.4
April 1997