Combinatorics
Combinations count how many ways to choose r items from n when order doesn't matter, using n! ÷ (r! × (n−r)!).
Combinations count how many ways to choose r items from n when order doesn’t matter, from lottery odds to poker hand counts, this calculator computes both the combination and the related permutation count.
Combinations count how many ways to choose r items from n when order doesn’t matter, using n! ÷ (r! × (n−r)!).
Permutations count arrangements where order matters (ABC is different from BCA), while combinations count selections where order doesn’t matter (ABC and BCA are the same selection). Since every combination of r items can be arranged in r! different orders, the permutation count is always the combination count multiplied by r!, this calculator shows both so you can see that relationship directly.
Lottery odds (choosing 6 numbers from 49, regardless of the order drawn), poker hand counts (choosing 5 cards from 52), and committee selection (choosing 3 people from 10) are all classic combination problems, included as quick-example presets in this calculator, since in each case the order of selection doesn’t change the outcome.
Combinations count selections where order doesn’t matter, while permutations count arrangements where order does matter, for the same n and r, permutations will always be a larger number since it also accounts for every possible ordering.
Because the order the numbers are drawn in doesn’t matter for winning, only which numbers were drawn, this makes it a combinations problem rather than a permutations problem.