Permutation & Combination Calculator
Count selections of distinct items with or without order.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Permutation & Combination Calculator
Choose combination mode when a selection is the same regardless of order, such as a committee. Choose permutation mode when positions matter, such as first, second and third place. Items must be distinct, and this calculator assumes selection without replacement. Exact integer arithmetic is used instead of rounding a potentially large count.
The calculation
Worked example
Choosing three people from ten gives 120 unordered groups. Assigning those three selections to different ordered positions gives 720 possibilities.
Assumptions and limits
Both inputs must be non-negative integers and r cannot exceed n. Selecting zero items has one outcome: the empty selection. The maximum n is 1,000. Repetition, indistinguishable objects, circular seating and restrictions on which items may be selected require different formulas and are outside this tool.
Common questions
Why are there more permutations?
Each chosen group can be arranged in r! different orders, so the permutation count is r! times the combination count.
Does this allow choosing the same item twice?
No. It counts selections without replacement. Repeated selections require another counting model.