Prove that, for N≥M≥n and
(N-M)≥n,
where C(a,b) = a! /(b! (a-b)! ) is the binomial coefficient.
This is one of the basic identities concerning sum of products of binomial coefficients: see the book The Art of Computer Programming (by Prof. Knuth) eq. 1.2.6.21.
Marco Corvi - 2003