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Permutation & Combination Calculator

Calculate nPr and nCr, with and without repetition, using exact big-number arithmetic.

Runs instantly in your browser — results update as you type.

What is the difference between permutation and combination?

In a permutation the order matters; in a combination it does not. Choosing 3 of 10 people gives C(10, 3) = 120 teams, but P(10, 3) = 720 ways to award gold, silver and bronze.

Formulas

  • nCr = n! ÷ (r! (n − r)!)
  • nPr = n! ÷ (n − r)!
  • With repetition: nʳ permutations and (n + r − 1)! ÷ (r! (n − 1)!) combinations.

Lottery example: picking 6 numbers from 49 has C(49, 6) = 13,983,816 combinations.

Frequently asked questions

How large can n be?

Up to 1,000 with exact results.

What is 0! ?

1, by definition.

Is it free?

Yes.