About this Permutation & Combination Calculator
Permutation & Combination Calculator computes exact counting results used in probability, arrangements and selection problems.
Formula or method
nPr = n!/(n−r)!; nCr = n!/[r!(n−r)!].
Example
For n=5 and r=2, permutations = 20 and combinations = 10.
Common uses
- Count ordered arrangements.
- Count unordered selections.
- Check probability and combinatorics exercises.
How to use this tool
- Enter the values or text requested by the calculator.
- Choose units or options when the tool provides them.
- Select the calculation button and review the result.
- Use the formula, example and notes on this page to check whether the result fits your situation.
Important note
Permutations care about order; combinations do not. Inputs must satisfy 0 ≤ r ≤ n.
Frequently asked questions
What is the difference between nPr and nCr?
nPr counts selections where order matters; nCr counts selections where order does not matter.
Can r be larger than n?
No. The selected number of items cannot exceed the available number.