Permutation & Combination Calculator interactive tool
Enter n and r
Results
For n = 10 and r = 3:
Permutations (nPr)720
Order matters. nPr = n! / (n − r)! counts ordered arrangements of r items chosen from n.
Combinations (nCr)120
Order does not matter. nCr = n! / (r! (n − r)!) counts unique groups of r items chosen from n.
What Is Permutation & Combination?
A permutation & combination calculator helps you quickly answer "how many ways" questions in counting and probability. It computes nPr (ordered arrangements) and nCr (unordered selections) based on factorial formulas.
Permutations vs. Combinations
- Permutations (nPr): Used when order matters. For example, arranging 3 students in a row from a class of 10 uses permutations.
- Combinations (nCr): Used when order does not matter. For example, choosing 3 toppings for a pizza from 10 options uses combinations.
Where You'll See Permutations & Combinations
These formulas appear in high school probability, competitive exams, card problems, and lottery-style counting puzzles. This permutation and combination calculator speeds up the arithmetic so you can focus on setting up the correct model for your problem.
How To Use the Permutation & Combination Calculator
- Enter a non-negative whole number for n, representing the total number of items.
- Enter a non-negative whole number for r, representing how many items are chosen from n.
- Confirm that r is not greater than n, otherwise the calculator will show an error.
- Review the nPr result for permutations (when order matters) and nCr result for combinations (when order does not matter).
- Use the Example button to load a typical probability problem setup, or Reset to clear the inputs and start again.