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Binomial Coefficient

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Binomial Coefficient Calculator

Our Binomial Coefficient Calculator finds "n choose k" — the number of ways to pick k items from a set of n items when order doesn't matter. It's the same value the nCr button on a scientific calculator produces.

What Is a Binomial Coefficient?

The binomial coefficient, written C(n, k) or (n choose k), counts how many distinct k-element subsets can be formed from a set of n elements. It's called "binomial" because these same numbers appear as the coefficients when expanding (x + y)ⁿ.

Binomial Coefficient Formula

C(n, k) = n! ÷ (k! × (n − k)!)

Where n! (n factorial) is the product of all positive integers up to n. Both n and k must be non-negative integers, with k no greater than n.

Example Calculation

n = 6, k = 2

C(6, 2) = 6! ÷ (2! × 4!) = 720 ÷ (2 × 24) = 15

✓ There are 15 ways to choose 2 items from 6

Features of Our Binomial Coefficient Calculator

✅ Handles large values of n and k accurately

✅ Shows both the result and the equation

✅ Instant, accurate results

✅ Free to use, no sign-up required

Who Can Use This Calculator?

Students & Teachers – For combinatorics and probability homework

Statisticians – For probability distributions and sampling problems

Programmers – For verifying combinatorics logic in code

Puzzle Solvers – For lottery odds and card-game combinations

👉 Try our Binomial Coefficient Calculator to find "n choose k" in seconds.