Permutation calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- nPr = n! ÷ (n − r)! = 10! ÷ 7!.
- That is the product of the r numbers starting at n: 720.
| Inputs | Answer |
|---|---|
| n: 10; r: 3 | P(10, 3) = 720. |
| n: 5; r: 5 | P(5, 5) = 120. |
| n: 26; r: 4 | P(26, 4) = 358,800. |
How to use it
A permutation counts the ordered ways to pick r items from n different items: nPr = n! ÷ (n − r)!. Order matters: picking A then B is different from picking B then A.
For 10 items taken 3 at a time, 10P3 = 10 × 9 × 8 = 720. Use the combination calculator when the order does not matter.
Frequently asked questions
What is 10P3?
10 × 9 × 8 = 720.
When do I use permutations?
When order matters, such as ranking the top 3 of 10 contestants.
What is the difference between a permutation and a combination?
Order counts in a permutation and does not count in a combination.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
About · How we verify this · Editorial policy · Corrections
General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.