I once read a very good explanation for the n! factor in the combinations formula but I can't find it. Can someone state the reason for it clearly please. ( N) = N!/n!/(N-n)! ( n) The N!/(N-n)! comes about because there are that many ways to choose n things from N. N for the first, N-1 for the second, ... N-n+1 for the nth. So far so good. There is a clear explanation for why this has 'double counted' and the n! term fixes it up.