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  N! / (K! * (N-K)!)
= (N * (N-1) * ... * (K+1)) / ((N-K) * (N-K-1) * ... * 1)

= exp((log N + log (N-1) + ... + log (K+1)) - (log (N-K) + log (N-K-1)
+ + ... + 0))