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Get NordVPN →Permutation Calculator (nPr)
Compute permutations nPr = n! / (n−r)!, the number of ordered ways to arrange r items chosen from n. Enter n and r (with 0 ≤ r ≤ n) to get an instant, exact result for any combinatorics problem.
Enter n and r to see the number of permutations.
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How it works
What is a permutation?
A permutation counts the number of ordered arrangements of r items selected from a set of n distinct items. Because order matters, choosing A then B is different from choosing B then A.
The formula is nPr = n! / (n−r)!. It requires 0 ≤ r ≤ n, since you cannot arrange more items than you have.
Permutations vs. combinations
Use permutations when the order of selection matters, such as ranking finishers in a race or assigning roles. Use combinations when order does not matter, like picking a committee.
Permutations always produce equal or larger counts than combinations for the same n and r, because each unordered group corresponds to several ordered arrangements.
Frequently asked questions
›What does nPr mean?
nPr is the number of permutations: ordered arrangements of r items chosen from n, calculated as n! / (n−r)!.
›How is nPr different from nCr?
nPr counts ordered arrangements where order matters, while nCr counts combinations where order does not matter.
›What if r equals n?
When r = n, nPr equals n!, the total number of ways to arrange all the items.
›Can r be 0?
Yes. nP0 equals 1, representing the single way to arrange zero items (the empty arrangement).
›What if r is greater than n?
That is not allowed. The formula requires 0 ≤ r ≤ n, because you cannot arrange more items than exist.
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