Permutations (nPr) Calculator
Use this free permutations (nPr) calculator to find the number of permutations. Enter total items (n) and the number of items to arrange (r), and get your result instantly.
What Are Permutations?
Permutations represent the number of ways to arrange items where order does matter. For example, arranging 2 fruits from {apple, banana, orange} results in different orderings like {apple, banana} and {banana, apple}, which are considered distinct.
Formula for Permutations (nPr)
The formula to calculate permutations is:
nPr = n! / (n − r)!
- n = total number of items
- r = number of items chosen
- ! = factorial, the product of all positive integers up to that number
Example Calculation
Example: How many ways can you arrange 3 students out of 8?
n = 8, r = 3
8P3 = 8! / (5!) = 8 × 7 × 6 = 336
There are 336 possible permutations.
Permutation vs Combination
| Feature | Combination | Permutation |
|---|---|---|
| Order Matters | No | Yes |
| Formula | nCr = n! / [r!(n−r)!] | nPr = n! / (n−r)! |
| Example | Choosing 2 fruits | Arranging 2 fruits |