Permutation & Combination Calculator (nPr, nCr)
Calculate permutations (nPr) and combinations (nCr), with or without repetition, exactly — even for very large numbers.
How to use
- 1Enter n (items to choose from) and r (how many are chosen).
- 2Choose whether items can repeat.
How it's calculated
nPr = n! ÷ (n − r)!. nCr = n! ÷ (r!(n − r)!). With repetition: permutations = nʳ, combinations = (n + r − 1)Cr.
Frequently asked questions
Permutation or combination?
Use permutations when order matters (race positions, PIN codes) and combinations when it doesn't (lottery numbers, a committee).
What are the odds of winning a 6/49 lottery?
There are 49C6 = 13,983,816 combinations, so one ticket has a 1 in 13,983,816 chance of the jackpot.
Can r be larger than n?
Only with repetition allowed. Without repetition you can't choose more items than you have.