Permutations & Combinations Calculator

About this calculator

This calculator finds both permutations (nPr = n!/(n−r)!), the number of ways to arrange r items from a set of n where order matters, and combinations (nCr = n!/(r!(n−r)!)), the number of ways to choose r items where order does not matter. The difference is exactly r! — combinations divide out the r! ways each same group could be ordered.

These are foundational tools in probability and statistics — used to compute lottery odds, card and dice game probabilities, the number of possible committees or teams, and password/combination-lock possibilities. Students use nPr and nCr constantly in probability coursework, while statisticians and data scientists use them when computing binomial probabilities and sampling scenarios. Enter n and r to get both values instantly.