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Combination & Permutation Calculator
Enter n and r to get combinations (nCr) and permutations (nPr).
Result
—
Number of ways.
| Combinations (nCr) | — |
|---|---|
| Permutations (nPr) | — |
| n! | — |
| Formula | — |
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How the Combination & Permutation Calculator Works
Both count the ways to choose r items from n, but they differ on order. A combination ignores order — picking players for a team, where the group is what matters — and uses n! / (r!(n−r)!). A permutation counts order — ranking finishers, or arranging letters — and uses n! / (n−r)!. This calculator gives both at once so you can pick the right one.
Permutations are always at least as many as combinations, because each combination can be arranged in several orders. For choosing 2 from 5, there are 10 combinations but 20 permutations.
nCr = n! ÷ (r!(n−r)!) · nPr = n! ÷ (n−r)!
Frequently Asked Questions
What is the difference between a combination and a permutation?
Order. Combinations treat the same items in any order as one; permutations count each ordering separately.
How do I calculate combinations?
Use n! divided by r! times (n−r)!. Choosing 2 of 5 gives 10 combinations.
When do I use permutations?
When the arrangement matters — rankings, passwords, seating orders. Choosing and ordering 2 of 5 gives 20 permutations.
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