Permutation Calculator
Compute nPr = n! ÷ (n − r)!: how many ordered arrangements of r items from n.
Calculator
Use the Permutation Calculator
Result
—
Formula
nPr = n! ÷ (n − r)!
Step-by-step
- 1
Enter n and r
n is the pool size, r is how many you pick.
- 2
Read the count
Ordered arrangements are shown.
Worked example
Example input: n: 10, r: 3
Result: 720
Related tools
- Combination Calculator
Same but order does not matter.
- Factorial Calculator
n! for any n.
Frequently asked questions
What does 10P3 equal?
720 — the number of ways to arrange 3 items out of 10 when order matters: 10 x 9 x 8, each step one choice smaller. Enter n = 10 and r = 3 above to see it.
Does order matter in a permutation?
Yes — that is the entire point: ABC is different from BAC here. When swaps should count as the same set, that is a combination instead, and the paired calculator handles it.
Why is P(n, n) equal to n factorial?
Arranging all n items means n choices for the first slot, n-1 for the second, and so on to 1 — that chain is exactly the factorial definition, n!.