Combination Calculator (nCr)
Calculate the number of combinations — the ways to choose r items from a set of n items where order does not matter.
Enter values for n and r to calculate combinations.
Combination Formula
C(n, r) = nCr = n! / ((n − r)! × r!)
A combination counts the number of ways to choose r items from n items where order does not matter. Choosing AB is the same as BA.
Permutation vs Combination
If order matters, use permutations (nPr). If order doesn't matter, use combinations (nCr). nCr is always less than or equal to nPr because multiple arrangements map to the same combination.
Example: How many ways to choose 3 items from 10?
C(10, 3) = 10! / (7! × 3!) = (10 × 9 × 8) / (3 × 2 × 1) = 120
C(10, 3) = 10! / (7! × 3!) = (10 × 9 × 8) / (3 × 2 × 1) = 120
When to Use Combinations
- Choosing a committee from a group
- Selecting lottery numbers
- Picking a team where roles don't matter
- Any selection where sequence is irrelevant
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Last updated: 2026-08-08