Calculate the number of ways to arrange r items from a set of n, where order matters.
How It Works
How Permutation Calculator (nPr) Works
A permutation counts every distinct ORDERED arrangement of r items chosen from n — since swapping the order creates a new outcome, this number is always larger than the equivalent combination count.
Worked Example
See It In Action
Arranging 2 medal positions among 5 racers (P(5,2)) gives 20 possible outcomes, since first place and second place are different roles.
FAQ
Frequently Asked Questions
Why is P(n,r) always bigger than C(n,r) for the same n and r?
Every combination of r items can be arranged in r! different orders, and a permutation counts each of those orderings separately — so P(n,r) = C(n,r) × r!, which is always at least as large.
