Permutation & Combination Calculator
Permutations (nPr) count the number of ways to arrange r items from a set of n, where order matters. Combinations (nCr) count the number of ways to choose r items from a set of n, where order does not matter.
This calculator computes both P(n,r) and C(n,r) using BigInt arithmetic for exact results, even for large values. These formulas are essential in probability, statistics, combinatorics, and many fields of mathematics and computer science.
How it works
P(n,r) = n! / (nâr)! â the number of ordered arrangements. C(n,r) = n! / (r! Ă (nâr)!) â the number of unordered selections. Also known as the binomial coefficient.
Use cases
- Calculating probability of lottery outcomes
- Determining possible arrangements in scheduling problems
- Solving counting problems in math competitions
- Computing binomial coefficients for polynomial expansion