Permutation and Combination Calculator
Calculate permutations and combinations for counting problems.
Counting the possibilities
Permutations and combinations count how many ways things can be arranged or chosen. This calculates both from the numbers you give, the tools behind probability, lottery odds, password strength and any question of how many possible outcomes there are.
Enter the total and the number chosen to calculate.
The crucial difference: does order matter?
The one thing to get right is whether order matters. A permutation counts arrangements where order matters — first, second and third place in a race are different outcomes. A combination counts selections where order does not — the three people chosen for a committee are the same group however you list them. Because permutations count more orderings of the same selection, there are always more permutations than combinations for the same numbers. Getting this distinction wrong is the commonest error in counting problems. Asking yourself whether rearranging the chosen items gives a genuinely different result tells you instantly which one you need.
Permutation and Combination Calculator FAQ
What is the difference between a permutation and a combination?
A permutation counts arrangements where order matters; a combination counts selections where it does not. Race places are permutations, a committee is a combination.
How do I know which to use?
Ask whether rearranging the chosen items gives a different result. If yes, it is a permutation; if not, a combination.
Is anything uploaded?
No. The calculation happens in your browser.