Permutations & Combinations Calculator

The calculator rounds r to the nearest whole number before using it in any factorial calculation, since you can't choose a fractional number of items. Nudging 3 up to 3.3 or down to 2.7 both round straight back to 3, so nothing about the computed permutation or combination actually changes until the input crosses the next whole integer.

Permutations count arrangements where order matters, so choosing item A then B is treated as different from B then A, giving the formula n! divided by (n minus r)!. Combinations count selections where order doesn't matter, dividing that same permutation count by r! to collapse every reordering of the same r items down to a single count.

Two different ceilings are at work here, and they're not the same one. JavaScript's standard number type can only represent whole numbers exactly up to about nine quadrillion, and a factorial-based result crosses that threshold around 18! to 19! — well before the 170-item mark. The engine's own factorial calculation additionally switches to the logarithmic path once n passes 170, since a true factorial that large would overflow to Infinity rather than merely losing precision. The logarithmic result sidesteps both ceilings by tracking the exponent of the answer instead of the answer itself, so relative magnitudes stay comparable even once n climbs into the hundreds.

A plain combination assumes every item in the pool of n can be chosen at most once, so you're always picking r distinct items. Combination with repetition allows the same item to be picked more than once — like scoops of ice cream where repeats are fine — and is computed instead as C(n plus r minus 1, r), a larger count than the no-repetition version for the same n and r.