🔀 Permutation & Combination Calculator
Calculate the number of permutations (nPr) and combinations (nCr) for choosing r items from a set of n items.
Values
Your Result
How the Permutation & Combination Calculator Works
Permutations count the number of ways to arrange r items from n items where order matters. Combinations count the number of ways to choose r items from n items where order does not matter.
Formulas
Combination: nCr = n! / (r! × (n − r)!)
Frequently Asked Questions
What's the difference between a permutation and a combination?
Permutations count arrangements where order matters (e.g. 1st, 2nd, 3rd place in a race). Combinations count selections where order doesn't matter (e.g. choosing 3 people for a committee).
What happens if r is greater than n?
It's impossible to choose more items than exist in the set, so both nPr and nCr are undefined (zero) when r > n.
Why does this calculator avoid computing full factorials?
Factorials grow extremely fast (e.g. 20! is over 2 quintillion), which can cause overflow or precision loss. This calculator computes the products iteratively so it stays accurate for larger values of n.