Permutations and Combinations Calculator
Use this when you pick some items from a bigger set and need to know how many ways that can happen. A combination counts groups where order does not matter, like a team. A permutation counts arrangements where order matters, like a race result.
- Free
- Works offline after your first visit
- Saves on this device
- No sign-up
- Updated
How it works
A combination is the number of ways to choose r items from n, with the order ignored. It is n! divided by r! times (n minus r)!, which is written as n choose r.
A permutation is the same count with the order kept, so it is n! divided by (n minus r)!. For the same numbers it is always at least as large as the combination.
Worked example
Choosing 3 items from 10 gives 120 groups where order does not matter, and 720 arrangements where it does.
Questions
What if I pick more items than I have?
The answer is zero, since there is no way to pick more items than exist.
Does the order of picks change a combination?
No. Picking A then B makes the same group as picking B then A. That is why a combination is smaller than a permutation.
Why do the numbers get so big?
Each extra item multiplies the count, so the totals grow fast. Enter the number of items you really have.
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