information:classification
Permutations of multisets

If M is a finite multiset, then a multiset permutation is an ordered arrangement of elements of M in which each element appears a number of times equal exactly to its multiplicity in M. An anagram of a word having some repeated letters is an example of a multiset permutation. If the multiplicities of the elements of M (taken in some order) are m 1 {\displaystyle m_{1}}, m 2 {\displaystyle m_{2}},..., m l {\displaystyle m_{l}} and their sum (that is, the size of M) is n, then the number of multiset permutations of M is given by the multinomial coefficient,

For example, the number of distinct anagrams of the word MISSISSIPPI is:

A k -permutation of a multiset M is a sequence of k elements of M in which each element appears a number of times less than or equal to its multiplicity in M (an element's repetition number).