Permutation Calculator

How to Use This Calculator

1. Enter the total number of distinct items `n`.
2. Provide how many positions `r` you wish to fill in order.
3. Ensure `r ≤ n`. The calculator returns zero if ordering more items than available.
4. Review the permutation count and supporting ratios to understand selection intensity.

Formula

• n! — factorial of the total items.
• (n − r)! — factorial of the unused items after placing r objects.
• The formula assumes no repetition; each object can be used at most once.

Full Description

Permutations count ordered arrangements of distinct items. They apply whenever order matters: ranking competitors, arranging books, or generating passcodes without repeats. The factorial structure grows rapidly — even small increases in `n` or `r` produce explosive counts.

Use permutations to model scenarios where each choice depends on the previous ones. When repetition is allowed, switch to `n^r` instead. For unordered selections, combinations (`C(n, r)`) provide the correct count.

Frequently Asked Questions