Permutation & Combination Calculator
Enter n and r to get both nPr (permutations) and nCr (combinations).
Permutations vs combinations
A permutation counts arrangements where order matters — picking a 1st, 2nd, and 3rd place from 10 runners. A combination counts selections where order doesn't matter — picking any 3 runners for a team, regardless of order. nCr is always nPr divided by r!.
About the Permutation & Combination Calculator
The Permutation and Combination Calculator computes nPr and nCr: the number of ways to choose r items from n, with order mattering (permutations) or not (combinations).
Permutations are used when order matters, like arranging people in a queue: nPr = n! / (n − r)!. Combinations are used when order does not matter, like choosing a committee: nCr = n! / (r! × (n − r)!). Because factorials grow quickly, results can become huge for large n.
How to use it
- Enter n, the total number of items.
- Enter r, the number chosen.
- Read nPr and nCr.
- Use the right one for your problem.
Tips and good to know
- r cannot exceed n.
- If order matters use permutations.
- nCr is always less than or equal to nPr.
Frequently asked questions
What is the difference between permutation and combination?
Order matters in permutations.
What is 0!?
It equals 1.
What if repetition is allowed?
Use different formulas, such as n to the power r.