Permutation & Combination Calculator interactive tool
For n = 10 and r = 3:
Order matters. nPr = n! / (n − r)! counts ordered arrangements of r items chosen from n.
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.
nPr and nCr for arrangements and selections
This permutation and combination calculator computes nPr when order matters and nCr when it does not. Enter n total items and r chosen items to check counting and probability problems.
Need the formula or convention behind this result? Read the calculator methods and assumptions.