Permutation Calculator (nPr)
By Santaji GadepatilinUpdated October 27, 2026
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How to use this calculator
Enter the total number of items and how many are chosen. The number of ordered arrangements is calculated.
Formula
nPr = n! ÷ (n − r)!
Worked example
Gold, silver and bronze from 10 runners:
10P3 = 10 × 9 × 8 = 720
More examples
| Situation | Calculation | Result |
|---|---|---|
| 4-digit PIN, no repeated digits | 10P4 | 5,040 |
| Arrange 5 books on a shelf | 5P5 | 120 |
| President, VP, secretary from 20 | 20P3 | 6,840 |
Frequently asked questions
What is a permutation?
An arrangement where order matters. Choosing a 1st, 2nd and 3rd place from 10 runners is a permutation.
What is the formula?
nPr = n! ÷ (n − r)!. For 10 and 3, 10 × 9 × 8 = 720.
How is it different from combinations?
Combinations ignore order. nPr = nCr × r!, so there are always more permutations than combinations.