Free Permutation Calculator
Calculate the number of permutations (ordered arrangements) when choosing r items from n items.
P(n, r)
720
n!3,628,800
C(n, r) for comparison120
P(n, r) vs Total Items (n)
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.
Example Calculation
How many ways can you arrange 3 books from a shelf of 10?
- 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)
Frequently Asked Questions
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