Combination Calculator

Enter n and r to get C(n,r): the number of ways to pick r items from n when order does not matter. No sign-up, no server. All calculation runs in your browser.

0-100
0 ≤ r ≤ n

When order does not matter

Combinations count selections only. Picking A then B is the same as B then A. Use C(n,r) for committees, lottery picks, or any “choose r from n” where the order of selection is irrelevant.

Formula: C(n,r) = n! / (r! x (n-r)!). Same as the binomial coefficient “n choose r”.

nCr vs permutations

Permutations P(n,r) treat order as important (e.g. first, second, third place). Combinations C(n,r) ignore order. For the same n and r, P(n,r) = C(n,r) x r!.

Typical uses

  • Choosing a subset (team, committee, sample)
  • Lottery or draw-style problems
  • Binomial coefficients and probability