Permutation Calculator Formula
Understand the math behind the permutation calculator. Each variable explained with a worked example.
Formulas Used
P(n, r)
permutations = factorial(n) / factorial(n - r)n!
n_factorial = factorial(n)C(n, r) for comparison
combinations = factorial(n) / (factorial(r) * factorial(n - r))Variables
| Variable | Description | Default |
|---|---|---|
n | Total Items (n) | 10 |
r | Items Chosen (r) | 3 |
How It Works
How to Calculate Permutations
Formula
P(n, r) = n! / (n - r)!
A permutation counts the number of ways to arrange r items chosen from n distinct items where order matters. For example, selecting a president, vice-president, and secretary from 10 people is a permutation problem because each position is different.
Worked Example
How many ways can you arrange 3 books from a shelf of 10?
n = 10r = 3
- 01P(10, 3) = 10! / (10 - 3)!
- 02= 10! / 7!
- 03= 10 * 9 * 8 = 720
- 04Compare with combinations: C(10,3) = 120 (order does not matter)
Ready to run the numbers?
Open Permutation Calculator