Permutation & Combination Calculator
Compare ordered arrangements with unordered selections and switch between no-repetition and repetition-allowed counting models.
Order and repetition determine the counting model
Permutations and combinations use the same n and r inputs but answer different questions. If rearranging the chosen items produces a different outcome, use the permutation count. If only the selected set matters, use the combination count.
The repetition switch changes the model rather than merely changing a coefficient: ordered selections become n^r, while unordered selections with repetition use C(n+r−1,r). Lynara uses exact BigInt arithmetic so large counts are not rounded through floating-point factorials.
Privacy: calculator inputs are processed in your browser; Lynara does not need to upload these values to calculate the result.
Formula
without repetition: nPr = n!/(n−r)!, nCr = n!/[r!(n−r)!]; with repetition: n^r and C(n+r−1,r)
Example
For n = 10 and r = 3 without repetition, 10P3 = 720 and 10C3 = 120.
Useful for
- nPr and nCr homework
- Counting ordered arrangements
- Counting unordered selections
- Combinatorics problems with repetition
Questions
What is the difference between a permutation and a combination?
A permutation counts arrangements where order matters; a combination counts selections where order does not.
What changes when repetition is allowed?
Ordered selections become n^r, while unordered selections with repetition use C(n+r−1,r).