Permutation Calculator
Calculate the number of possible arrangements of r items from a set of n items.
Enter Your Values
Table of Contents
Permutation Formula
A permutation is an arrangement of objects in a specific order. The number of permutations of r items from a set of n items is given by:
Where:
- n is the total number of items
- r is the number of items to arrange
- ! represents factorial
How to Calculate Permutations
To calculate permutations, follow these steps:
-
1Identify the total number of items (n)
-
2Determine how many items to arrange (r)
-
3Calculate n! (factorial of n)
-
4Calculate (n-r)! (factorial of n-r)
-
5Divide n! by (n-r)! to get the number of permutations
Understanding Permutations
Key points about permutations:
-
1Order Matters:
In permutations, the order of arrangement is important.
-
2No Repetition:
Each item can only be used once in the arrangement.
-
3Factorial Growth:
The number of permutations grows very quickly with n and r.
Practical Examples
Example 1 Race Positions
n = 5 runners
r = 3 positions (1st, 2nd, 3rd)
P(5,3) = 60
There are 60 possible ways to arrange 3 runners from 5.
Example 2 Password Creation
n = 10 digits (0-9)
r = 4 positions
P(10,4) = 5,040
There are 5,040 possible 4-digit passwords without repetition.
Example 3 Committee Selection
n = 8 people
r = 3 positions (President, Vice-President, Secretary)
P(8,3) = 336
There are 336 possible ways to fill these 3 positions.