Binomial Coefficient Calculator

Calculate nCr and nPr values with Pascal's triangle row visualization.

n (total)

r (choose)

Tab to move between fields

C(n, r)

120

P(n, r)

720

Pascal Row Length11

How to Use This Calculator

Enter n (the total number of items) in the top field.
Enter r (the number of items to choose) — must satisfy 0 <= r <= n.
Review C(n, r) — the number of r-combinations — and P(n, r) — the number of r-permutations.
Check the Pascal Row Length to see where C(n, r) falls in Pascal's triangle.
Use these values in probability, combinatorics proofs, or algorithm analysis.

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