Permutation Calculator
P(n,r) = n! / (n−r)!. Click any i for detail.
n and r
n
i
n
Size of the set. Need n ≥ r ≥ 0. |
|
|---|---|
r
i
r
How many you arrange. |
How to use this calculator
- Enter n and r.
- Read nPr permutations.
- Compare nCr when order does not matter.
- Require 0 ≤ r ≤ n.
Results explained
Permutations count ordered arrangements. nPr = n! / (n−r)!. Race finishes and lock codes are permutation problems.
Quick reference: nPr
P(10,3) = 720 ordered triples.
| Item | Detail |
|---|---|
| nPr | order matters |
| nCr | order ignored (shown beside) |
| P(n,n) | n! permutations of all |
| P(n,1) | = n |
Large factorials can exceed safe JS integers.
How the estimate is built
P(n,r) = n! / (n−r)!.
Example scenario
P(10,3) → 720.
FAQ
Lottery tickets: permutation or combination?
Most lotto draws are combinations unless order is printed on the ticket.
What if r = 0?
P(n,0) = 1: one empty arrangement.
Can r exceed n?
No. You cannot arrange more items than exist.