Combination Formula
C(n, r) = n! / (r! × (n − r)!)
Where n is the total number of items and r is the number chosen.
Example
C(10, 3) — Choosing 3 from 10
C(10,3) = 10! / (3! × 7!) = (10 × 9 × 8) / (3 × 2 × 1) = 720 / 6 = 120
Combination vs Permutation
| Order matters? | Formula | |
|---|---|---|
| Combination | No | C(n,r) = n! / r!(n−r)! |
| Permutation | Yes | P(n,r) = n! / (n−r)! |