Anagram

An anagram of a finite string is another string with exactly the same number of occurrences of each symbol. Thus $aab$ and $aba$ are anagrams; $abb$ is not. Equivalently, the second string is obtained by a permutation of the positions.

If a length-$n$ string has symbol multiplicities $m_1,\dots ,m_r$, its number of distinct anagrams is the multinomial coefficient $n!/(m_1!\cdots m_r!)$. Dividing by the factorials removes position permutations that only exchange equal symbols. The count depends on multiplicities, not the original ordering.