Binomial coefficient C(n, k)

Calculate "n choose k" — the number of ways to choose k items from n items without regard to order.

C(,)

C(n,k) = n! / (k! × (n−k)!)

C(10,3) = 10! / (3! × 7!) = (10×9×8) / (3×2×1) = 720/6 = 120.

C(n,0) = C(n,n) = 1. C(n,k) = C(n,n−k) (symmetry). C(n,1) = n.