Permutation and Combination Calculator
Work out nPr and nCr: how many ways to arrange or choose items.
Order matters, or it does not
A permutation counts arrangements, so choosing A then B is different from B then A. A combination counts selections, so A and B together is the same group either way.
The formulas
nPr = n! ÷ (n − r)! and nCr = n! ÷ (r! × (n − r)!). The factorial n! means n × (n − 1) × … × 1.
Example
Choosing 3 people from 10 for a committee, where order does not matter, can be done in 120 ways. Awarding gold, silver and bronze to 3 of the 10 people, where order does matter, can be done in 720 ways.
Frequently asked questions
What is 0 factorial?
By definition 0! = 1, which makes the formulas work when you choose nothing or everything.
Why is nCr smaller than nPr?
Each group of r items can be arranged in r! ways, so nPr = nCr × r!.
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