Permutation and Combination Calculator
Count the ways to choose or arrange r items from n — permutations (order matters) and combinations (order does not) — exactly, however large.
Result
Enter n and r.
How to use this calculator
- Enter n (total items) and r (items chosen).
- See combinations, permutations, and both with repetition allowed.
Formula
- Combinations: C(n, r) = n! ÷ (r! (n − r)!)
- Permutations: P(n, r) = n! ÷ (n − r)!
- With repetition: nʳ arrangements and C(n + r − 1, r) selections.
Worked example
Poker hands
The number of 5-card hands from a 52-card deck is C(52, 5) = 2,598,960. Choosing 2 of 5 gives 10 combinations and 20 permutations.
Assumptions and limitations
- Everything runs in your browser; nothing you enter is uploaded or stored.
- Results are exact; very long numbers are also shown in scientific notation.
Frequently asked questions
When does order matter?
Use permutations for rankings, codes and seating plans; use combinations for teams, lottery numbers and hands of cards.
What if r is larger than n?
Without repetition there are no ways to choose, so nPr and nCr are 0.