Combinatorics, Permutations With Repeated Elements

Permutations With Repeated Elements

When k out of n elements are indistinguishable, e.g. k copies of the same book, the number of different permutations is n!/k!. If we (temporarily) distinguish the k elements, e.g. number the copies of David Coperfield, there are again n! permutations. But the order of the k copies doesn't really matter, so k! permutations map onto 1. Thus we obtain n!/k!.

A similar factor must be included for each group of repeated elements. For example, The number of permutations of the letters "JJJKLMMN" is 8!/3!/2! = 3360.