Editing Permutation (section)

===Permutations of multisets===
[[File:Permutations with repetition cropped.svg|thumb|Permutations without repetition on the left, with repetition to their right]]

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.{{efn|The natural order in this example is the order of the letters in the original word.}} If the multiplicities of the elements of ''M'' (taken in some order) are <math>m_1</math>, <math>m_2</math>, ..., <math>m_l</math> 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#Multinomial coefficients|multinomial coefficient]],<ref>{{harvnb|Brualdi|2010|loc=p. 46, Theorem 2.4.2}}</ref>
:<math>
  {n \choose m_1, m_2, \ldots, m_l} =
  \frac{n!}{m_1!\, m_2!\, \cdots\, m_l!} =
  \frac{\left(\sum_{i=1}^l{m_i}\right)!}{\prod_{i=1}^l{m_i!}}.
</math>

For example, the number of distinct anagrams of the word MISSISSIPPI is:<ref>{{harvnb|Brualdi|2010|p=47}}</ref>
:<math>\frac{11!}{1!\, 4!\, 4!\, 2!} = 34650</math>.

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'').