Permutation & Combination Calculator

Order matters in permutations, not in combinations. Picking 1st, 2nd, 3rd from 5 runners is a permutation (5P3 = 60); picking any 3 friends from 5 for a team is a combination (5C3 = 10).

Whether the same item can be picked more than once. A 3-digit lock code allows repetition (10³ = 1,000 codes); dealing 3 cards from a deck doesn’t (52P3 = 132,600 ways).

You can’t pick 5 distinct items out of 3 — you’d run out. With repetition allowed, r can exceed n (like a 10-digit code from 10 digits).

Enormous — factorials grow faster than exponentials. The calculator uses exact integer arithmetic (BigInt), so even a 29-digit answer like 100C50 = 100,891,344,545,564,193,334,812,497,256 is exact, not rounded.

Both equal 1. There’s exactly one way to choose nothing from nothing — the empty selection. It also keeps the formulas consistent (0! = 1).