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(Useful formulas)
Beyond the basic formula, several identities simplify combination calculations. C(n,k) = C(n,n-k) is symmetry.
Pascal's identity: C(n,k) = C(n-1,k-1) + C(n-1,k). Sum identity: C(n,0) + C(n,1) + ... + C(n,n) = 2^n.
Vandermonde identity: C(m+n,k) = sum of C(m,i) × C(n,k-i) for i from 0 to k. These identities solve complex counting problems.
