Permutation Calculator

Calculate the number of permutations (ordered arrangements) of r items selected from a set of n items. A permutation is an arrangement where order matters.

How to Use This Calculator

1. Enter the total number of items (n) in the first field
2. Enter the number of items you want to select (r) in the second field
3. Click "Calculate Permutation" to see the result
4. The formula and step-by-step calculation will be displayed

What are Permutations?

A permutation is an ordered arrangement of objects. The number of permutations of r items selected from n items is calculated using the formula:

P(n, r) = n! / (n - r)!

Where n! (n factorial) means n × (n-1) × (n-2) × ... × 2 × 1

Examples

• P(5, 3): How many ways can you arrange 3 items from 5? Answer: 60 ways
• P(10, 2): How many ways can you arrange 2 items from 10? Answer: 90 ways
• P(7, 7): How many ways can you arrange all 7 items? Answer: 5,040 ways

Permutations vs Combinations

The key difference between permutations and combinations is that permutations consider order while combinations do not. For example, selecting items A, B, C in that order is different from selecting C, B, A in permutations, but they are the same in combinations.