Permutation and Combination Calculator: nPr and nCr Explained
2026-05-24
Quick Answer
Quick Answer: Permutations P(n,r) count ordered arrangements; combinations C(n,r) count unordered selections. Example: C(10,3) = 120. Calculate both with our Permutation & Combination Calculator.
Formulas
| Type | Formula | Meaning |
|---|---|---|
| Permutation | P(n,r) = n! / (n−r)! | Order matters |
| Combination | C(n,r) = n! / (r!(n−r)!) | Order does not matter |
Real-world examples
Lottery-style selection
Choose 6 numbers from 49 without order → C(49,6) possibilities.
Podium finishes
Gold, silver, bronze from 8 runners with order → P(8,3) = 8×7×6 = 336.
Committee of 3
Pick 3 people from 10 for a team where roles are equal → C(10,3) = 120.
Try It Yourself
Run your numbers through the Permutation & Combination Calculator. Also see Random Groups for splitting lists.
Frequently Asked Questions
When is order important?
Lineups, passwords, rankings → permutations. Committees, ingredient subsets, hand of cards → combinations.
What if n < r?
The calculator shows an error— you cannot pick more items than exist.
Large numbers?
Factorials grow fast; very large n may exceed display limits. Typical homework sizes (n ≤ 50) work fine.
Try it yourself
Use our free Permutation & Combination Calculator — no signup required.
Open Permutation & Combination Calculator →