Permutations Calculator

Permutations are used when the order of items matters.

Formula: nPr = n! / (n-r)!

Example: How many ways can you arrange 3 books from a shelf of 5 books?

This is a permutation problem because the order matters (ABC is different from BAC).

Result:

60

Calculation steps:

5P3 = 5! / (5-3)!

= 5! / 2!

= 120 / 2

= 60

This tool calculates how many ways you can arrange a set of items when order matters.

How Does It Work?

The tool uses the formula nPr = n! / (n-r)!.

You give the total number of items (n) and the number of items you want to select (r).

It then calculates the number of arrangements.

How to Use This Tool

Follow these steps to get your answer:

  1. Enter the total number of items in the field marked n.

  2. Enter the number of items to arrange in the field marked r.

  3. Click the Calculate button.

  4. See the result appear below.

Input Field Explanation

The n field accepts the total count of items. Type a whole number.

The r field accepts the count of items to select for the arrangement. Type a whole number.

Output Description

The result shows the number of different orders. The tool displays each step of the calculation.

For example, for 5 items with 3 selected, it shows:

Common Use Cases

This calculator helps when you need to plan seating, arrange tasks, or order books from a shelf.

It is handy for students and professionals who work with ordered data.

Limitations and Special Notes

Both input numbers must be zero or positive. The tool does not work if r is larger than n.

If you enter a value where r is larger than n, you will see an error message.

This guide shows you how to get clear results quickly.