Permutation and Combination Calculator
Work out nPr, nCr and factorials with the full working.
Calculate
How to use this calculator
Enter the total number of items n and the number you choose r. You get permutations (order matters), combinations (order does not matter) and factorials.
How it's calculated
P(n, r) = n! ÷ (n − r)! and C(n, r) = n! ÷ (r! × (n − r)!). Arrangements with repetition are nʳ.
Worked example
Choosing 3 people from 10: C(10, 3) = 120 teams, but P(10, 3) = 720 ways to give them first, second and third place.
Frequently asked questions
When do I use permutations?
When order matters, like race positions or passwords.
When do I use combinations?
When order does not matter, like picking a committee.
Related tools
Last updated October 2026. Results are for learning and guidance; always check important work. Calculations run in your browser and are not stored.