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Math

Permutations Calculator

Count ordered arrangements of k distinct items chosen from n without replacement.

Exact method explained belowEditable inputs

Set up your calculation

Runs on your device

SOLUTION

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter available items n, positions k.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

P(n,k) = n! ÷ (n − k)!. Each change in order counts as a different arrangement.

A WORKED EXAMPLE

Filling 3 ordered positions from 10 distinct items gives 720 permutations.

What to keep in mind

Inputs must satisfy 0 ≤ k ≤ n ≤ 500. This excludes replacement and does not adjust for repeated identical objects.

Common questions

How is this different from combinations?

Permutations count order. Combinations count only which items are selected.

What if every item is arranged?

Setting k = n gives n!, the factorial of the number of distinct items.

Methodology maintained by ClarityKit. How these tools are built and checked.