Permutation & Combination Calculator
Calculate how many ways you can arrange or choose items — permutations (order matters) and combinations (order doesn't).
Show solution steps
What is the Permutation & Combination Calculator?
Permutations and combinations both count the number of ways to select r items from a group of n, but differ on whether order matters. Permutations (nPr) count arrangements — like how many ways 3 runners can finish 1st, 2nd and 3rd out of 10 — where swapping the order creates a different outcome. Combinations (nCr) count selections — like how many different 3-person committees can be formed from 10 people — where order doesn't matter at all.
How to Calculate
Enter n (the total number of items) and r (how many you're choosing or arranging). Permutations are computed as n! ÷ (n−r)!, and combinations as n! ÷ (r! × (n−r)!) — the combination formula divides the permutation count by r! to remove all the orderings of the same r items, since order no longer matters.
Formula
nPr = n!/(n−r)! nCr = n!/(r!(n−r)!)
How to Use
- Enter your details in the fields above.
- The result updates instantly as you type.
- Use Copy, Print or Download PDF to save your result.