Enter n and r to get permutations (nPr), combinations (nCr) and n factorial.
Understanding the permutation and combination calculation
This calculator finds how many ways you can arrange or choose items. Permutations count ordered arrangements; combinations count unordered selections.
Enter the total items n and how many you pick, r.
How to fill it in
- Enter n, the total number of items.
- Enter r, how many you choose.
- Read nPr, nCr and n factorial.
Formula reference
nPr = n! ÷ (n−r)!
nCr = n! ÷ (r! × (n−r)!)
Worked example
On the values this calculator opens with, the permutations nPr is 720. Underneath, Combinations nCr comes out at 120 and n! at 3.63M. Change any field and every figure updates as you type.
Frequently asked questions
What’s the difference between permutations and combinations?
Permutations count order (AB ≠ BA); combinations don’t (AB = BA). There are always at least as many permutations as combinations.
What is a factorial?
n! is the product of all whole numbers from 1 to n. 5! = 120.
When would I use nCr?
Any time order doesn’t matter — lottery picks, choosing a committee, dealing a hand of cards.