Permutation combination guide

Permutation and Combination Calculator Guide

The Permutation and Combination Calculator finds nPr and nCr from the same n and r inputs so you can compare order-matters and order-does-not-matter counts.

Open the permutation and combination calculator

Quick start

Enter n, the total number of items.
Enter r, the number of items selected.
Press Calculate nPr and nCr.
Use the permutation answer when order matters and the combination answer when order does not matter.

Permutation vs combination

A permutation counts arrangements, so ABC and BAC are different outcomes. Use nPr when the order matters.

A combination counts groups, so ABC and BAC are the same group. Use nCr when the order does not matter.

Using counting in probability

Many probability problems compare favorable outcomes with total possible outcomes.

Permutations and combinations help count those outcomes without listing every case one by one.

Examples from the calculator

Choose 3 from 10 10P3 and 10C3

720 permutations, 120 combinations

Cards example 52C5

2,598,960 combinations

Podium order 8P3

336 permutations

History, privacy, and copying

Recent answers stay visible in the page while you work. The history is kept only in the current browser tab and is not sent to a server.

Copy answer copies the expression and result so you can paste it into notes, homework, a message, or another document.