Binomial Coefficient Calculator

Calculate C(n,k) = n!/(k!(n-k)!)

n (total items)

k (items to choose)

Basic Formula

C(n,k) = n! / (k! × (n-k)!)

Combination formula

Alternative Notation

(n choose k) = nCk

Common notations

Symmetry Property

C(n,k) = C(n, n-k)

Useful for optimization

Pascal's Identity

C(n,k) = C(n-1,k-1) + C(n-1,k)

Recursive relation

Combinatorics

• Choosing combinations

• Counting problems

• Pascal's triangle

Probability

• Binomial distribution

• Probability calculations

• Statistical analysis

Algebra

• Binomial theorem

• Polynomial expansion

• Series calculations

C(n, 0) = 1

C(n, 1) = n

C(n, n) = 1

C(n, 2) = n(n-1)/2

C(n, n-1) = n

C(n, k) = 0 if k > n