nPr and nCr, with or without repetition
Enter n (the set size) and r (how many are taken) to get both the permutation and combination count at once, with a toggle for whether repetition is allowed — every result is exact, computed with BigInt.
How to use
- Enter n and r
- Choose whether repetition is allowed
- Press Calculate for both nPr and nCr, with the formula worked through below
Common questions
How do I know whether I want a permutation or a combination?
Ask whether swapping two of your picks would give a genuinely different result. If order matters — a race finish or a lock code — you want the permutation (nPr). If it doesn't — a team or a lottery draw — you want the combination (nCr), which is always the smaller of the two numbers.
What does "with repetition" change?
Without it, each pick removes one option from what's available for the next pick (like dealing cards). With it, every pick is made from the full set again, so the same item can be chosen more than once (like rolling a die multiple times) — this changes both formulas, not just the numbers.
How large can n and r be?
Up to 500 each. Every calculation runs on BigInt, so results are exact rather than rounded, even when they run to hundreds of digits.