Combinations (nCr) Calculator

About this calculator

nCr, read n choose r, counts the number of distinct ways to select r items from a set of n distinct items when the order of selection doesn't matter, computed as n! ÷ (r! × (n−r)!). It differs from permutations, which count arrangements where order does matter, by dividing out the r! ways any chosen subset could itself be ordered.

Combinations are the backbone of probability calculations wherever outcomes are unordered groups: computing lottery odds, such as choosing 6 numbers from 49, evaluating poker hand probabilities where a 5-card hand is a combination of 5 from 52, sampling statistics in quality control and clinical trial design, and counting the number of possible committees, teams, or subsets that can be formed from a larger group.

Enter n and r and this calculator returns nCr, the exact number of possible combinations.