Permutation & Combination Calculator

Permutations and combinations are fundamental concepts in combinatorics. A permutation (nPr) counts the number of ways to arrange r items from n, where order matters — for example, the number of ways to assign 1st, 2nd, and 3rd place from 10 competitors. A combination (nCr) counts ways to choose r items from n where order does not matter — like picking 3 members from a group of 10.

The formulas are: nPr = n! / (n-r)! and nCr = n! / (r! × (n-r)!). This calculator uses JavaScript's BigInt for exact integer arithmetic, avoiding floating-point rounding errors that affect standard Number for large factorials. Values of n up to 20 are supported (20! = 2,432,902,008,176,640,000).

The step-by-step formula display shows all intermediate factorial values so you can follow the calculation manually or verify your work.

You may also find our Scientific Calculator and Random Number Generator helpful.