Calculate combinations (order does not matter) and permutations (order matters) for any n and r, the foundation of counting and probability.
How it works
- Enter the total number of items (n).
- Enter the number of items you are choosing (r).
- The engine computes the combinations and permutations formulas instantly.
Frequently asked questions
Combination vs permutation?
Use combinations when order does not matter (a committee of 3), permutations when it does (1st, 2nd, 3rd place).
Why does n cap at 170?
Beyond 170!, the factorial exceeds JavaScript's number range. Larger cases need big-integer math.
Where is this used?
Lottery odds, poker hands, password counting, and any "how many ways" question.
When do I use combinations vs permutations?
Use combinations when order doesn't matter (choosing a committee); use permutations when it does (awarding first, second, third place).
What is the formula for combinations?
C(n, r) = n! / (r! × (n−r)!). This counts the number of ways to choose r items from n items when order does not matter. The calculator handles the factorial arithmetic automatically.