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.
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.
Frequently Asked Questions (FAQ)
What is the difference between nPr and nCr?
nPr counts permutations, where the order of the chosen items matters. nCr counts combinations, where the order does not matter. This tool shows both.
Is this permutations and combinations calculator free?
Yes. It is free to use, runs in your browser, and needs no signup.
Are there limits on n and r?
Yes. n and r must be non-negative whole numbers, r cannot be bigger than n, and n must be 170 or less to keep the result in range.
Does the tool show the working steps?
Yes. It shows nPr as n! divided by (n-r)!, nCr as nPr divided by r!, and the value of n! itself.