Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
Start With One Question: Does Order Matter?
Use a permutation when the arrangement matters, such as assigning gold, silver, and bronze medals. Use a combination when only the chosen group matters, such as selecting three students for a committee.
A Simple Example
From 10 people, choosing 3 ranked winners gives 720 permutations because first, second, and third place are different roles. Choosing 3 committee members gives only 120 combinations because the same three people count as one group no matter the order.
What the Inputs Mean
- = total items available
- = items chosen
- = multiply all positive integers from 1 through
The calculator requires non-negative integers and because you cannot choose more distinct items than exist.
Frequently asked questions
How do I know whether to use permutation or combination?
Ask whether rearranging the same chosen items creates a new outcome. If yes, use a permutation. If no, use a combination.
Why must r be less than or equal to n?
You cannot choose more distinct items than exist in the available set. The calculator blocks that case instead of returning a misleading count.
Why are permutations usually larger than combinations?
Because permutations count every order separately, while combinations treat the same selected group as one result.
What does 0! mean?
By convention, 0! = 1. That keeps the formulas consistent for cases such as choosing zero items or choosing all available items.
