Permutation and Combination Calculator
Calculate permutations P(n,r) and combinations C(n,r) — with and without repetition. Find how many ways to arrange or select r items from n distinct items.
Input
P(n,r) — Permutation
720
without repetition
C(n,r) — Combination
120
without repetition
Pᵣₑₚ — Permutation
1,000
with repetition (nʳ)
Cᵣₑₚ — Combination
220
with repetition
| Type | Formula | Order matters? | Repetition? |
|---|
| Permutation | n! / (n−r)! | Yes | No |
| Combination | n! / (r!(n−r)!) | No | No |
| Perm (rep) | nʳ | Yes | Yes |
| Comb (rep) | C(n+r−1, r) | No | Yes |
Step-by-step
| Property | Calculation | Value |
|---|
| P(10,3) | 10! / (10−3)! = 10! / 7! | 720 |
| C(10,3) | 10! / (3! × 7!) | 120 |
| Pᵣₑₚ(10,3) | 10^3 | 1,000 |
| Cᵣₑₚ(10,3) | C(12,3) | 220 |
Pascal's Triangle (C(n,r))
| n\r | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|
| 0 | 1 | | | | | | | |
| 1 | 1 | 1 | | | | | | |
| 2 | 1 | 2 | 1 | | | | | |
| 3 | 1 | 3 | 3 | 1 | | | | |
| 4 | 1 | 4 | 6 | 4 | 1 | | | |
| 5 | 1 | 5 | 10 | 10 | 5 | 1 | | |
| 6 | 1 | 6 | 15 | 20 | 15 | 6 | 1 | |
| 7 | 1 | 7 | 21 | 35 | 35 | 21 | 7 | 1 |