Permutation and Combination Calculator
Combinations count groups where order does not matter, like lottery numbers; permutations count arrangements where order matters, like the podium of a race.
How to use it
- Type the total number of items, n.
- Type how many are chosen, r.
- Read the four results and pick the one that matches your problem.
Frequently asked questions
What are the formulas?
Combinations: C(n, r) = n! / (r! (n − r)!). Permutations: P(n, r) = n! / (n − r)!. With repetition: C(n + r − 1, r) combinations and nʳ permutations.
How many lottery combinations are there?
Choosing 6 numbers out of 60 gives C(60, 6) = 50,063,860 combinations, so one ticket has a 1 in 50,063,860 chance. For 6 out of 49 the count is 13,983,816.
When is repetition allowed?
When the same item can be chosen again, like digits in a PIN code (10⁴ = 10,000 permutations) or scoops of ice cream of the same flavour (combinations with repetition).
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