Permutations and Combinations Calculator
Solve nPr and nCr problems on one page. Enter the total number of items (n) and how many you choose (r) — the calculator shows permutations where order matters and combinations where it does not, with the working steps displayed.
Enter values — the result will show live here.
How to use
- Enter n (the total number of items) and r (how many you choose). Keep r equal to or smaller than n.
- nPr appears for arrangements where order matters, and nCr for selections where order does not — both update live.
- Check the working steps shown under the result to see the factorial calculation, which helps with homework and exam practice.
Note: Formulas: nPr = n! / (n-r)! and nCr = n! / (r! x (n-r)!). For very large n the result gets too big, so n is limited to 170 here to avoid overflow.
Tips
- Use nPr when order matters — passwords, rankings and seating arrangements.
- Use nCr when order does not matter — lottery numbers, teams and committees.
- Make sure r is not larger than n; the result is meaningless otherwise.