Permutation Calculator
Calculate the number of permutations (nPr) — the number of ways to arrange r items from a set of n items, where order matters.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Your result
60
Number of permutations (nPr)
AI explanation
Formula
nPr = n! / (n − r)!Worked example
Choosing and arranging 3 items from 5
| Field | Value |
|---|---|
| Total items (n) | 5 |
| Items chosen (r) | 3 |
| Number of permutations (nPr) | 60 |
| Number of combinations (nCr) | 10 |
Assumptions
- Order matters in a permutation — arranging items ABC differently (ABC vs BCA) counts as different permutations. If order doesn't matter, use the number of combinations shown instead.
- r cannot be greater than n.
Frequently asked questions
What is a permutation?
A permutation is an ordered arrangement of items — choosing 3 items from 5 and arranging them in a specific order gives more possible outcomes (permutations) than just choosing which 3 items (combinations), since each selection can be arranged in multiple orders.
When should I use permutation instead of combination?
Use permutation when the order of selection matters — like assigning 1st, 2nd, and 3rd place in a race. Use combination when only the group of selected items matters, not their order — like picking a committee of 3 people.
How is nPr related to factorial?
nPr = n! / (n−r)! — it's the factorial of n, with the factorial of the "unused" items (n−r) divided out.