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.