How to use Permutations and Combinations Calculator
- Enter the number of available types and the number of selections.
- Choose whether order matters.
- Choose whether repeated selections are allowed.
- Review the formula, zero-case handling and exact count.
Example: Permutations and Combinations Calculator
Choose three distinct items from five without ordering.
You add
Available types: 5. Selections: 3. Mode: combinations without repetition.
You get
The count is C(5,3) = 10. Ordered selection without repetition would give 60.
Supported inputs and limits
n and k are whole numbers from 0 to 500; without repetition k cannot exceed n. Counts use exact BigInt arithmetic and can be long. With repetition, permutations use n^k and combinations use C(n+k−1,k), with empty-selection cases handled explicitly. Items are distinguishable types; no probability or ranking is inferred.
Where your input is processed
This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.
Questions about Permutations and Combinations Calculator
When does order matter?
Choosing A then B is different from B then A for a permutation. A combination treats those as one selection.
What does repetition mean here?
A type may be selected more than once. Without repetition, each available type can be used at most once.
Why is selecting zero items counted as one?
There is one empty selection or arrangement. The tool treats that case explicitly instead of dividing by a missing factorial.