What is the formula for permutations?
P(n, k) = n! / (n − k)!, which multiplies n by n − 1 and so on for k terms. For example, choosing a gold, silver and bronze medallist from 10 runners is P(10, 3) = 720.
Permutation and Combination Calculator
Count ordered arrangements P(n, k) and unordered selections C(n, k) exactly, even when the numbers are large.
Runs in your browser — nothing is uploaded
About the Permutation and Combination Calculator
A permutation counts the ways to pick k items from n when order matters, such as finishing positions in a race. A combination counts the same selections when order does not matter, such as choosing a committee. Combinations are always smaller because each group corresponds to several orderings.
The calculator uses exact integer arithmetic rather than floating-point approximations, so the answers are correct for large values. For n up to 25 it also shows n factorial, which underlies both formulas.
FAQ
Permutation and Combination Calculator — frequently asked
What is the formula for combinations?
C(n, k) = n! / (k! (n − k)!). Choosing 3 people for a team of 10 is C(10, 3) = 120, because the order of selection does not change the team.
What if repetition is allowed?
This calculator assumes no repetition. With repetition, the count of ordered selections is n^k, and the count of unordered selections uses C(n + k − 1, k). Those are different formulas.
Why is k larger than n an error?
You cannot choose more distinct items than you have without repetition, so the count is zero. The calculator asks you to keep k at or below n.
Why does the calculator limit n to 300?
Factorials grow extremely fast. Beyond about 300, the results have hundreds of digits and are rarely useful on screen, so the limit keeps the display readable.
Is my input stored?
No. The numbers are calculated in your browser and nothing is saved.
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