What is a permutation?

A permutation is an arrangement of objects where order matters. Selecting President, VP, and Secretary from a group is a permutation because the positions are different.

How is permutation different from combination?

In permutations, order matters (ABC ≠ BAC). In combinations, order doesn't matter (ABC = BAC). Use permutations for rankings, sequences, passwords.

What does 'with repetition' mean?

With repetition, items can be reused. For a 4-digit PIN using digits 0-9, each position can use any digit, so it's 10^4 = 10,000 possibilities.

When should I use permutations?

Use permutations when order matters: arranging books on shelf, race placements, password characters, seating arrangements, phone numbers.

What if n = r in permutations?

nPn = n! (factorial). This gives all possible arrangements of n items. For 5 books on a shelf: 5! = 120 arrangements.

Permutation Calculator

Calculate permutations (nPr) - arrangements where order matters.

Total Items (n)

Total number of items to choose from

Items to Arrange (r)

Number of positions to fill

Type

Each item can only be used once

Arrangement

10P3

0

= 0

nPr

10P3

10!

(n-r)!

(10-3)!

5,040

Step-by-Step Calculation

10×9×8=0

Documentation

Understanding Permutations

Permutations count the number of ways to arrange r items from a set of n items when order matters. Each arrangement is unique.

Without Rep

With Rep

All Items

Frequently Asked Questions

How to Use

About the Permutation Calculator

What it calculates

This permutation calculator solves mathematical and statistical problems using standard formulas. Calculate arrangements with or without repetition (nPr).

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Permutation Calculator.

Explore More

Permutation Calculator

Type

Arrangement

0

Step-by-Step Calculation

Understanding Permutations

About the Permutation Calculator

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