Combination and Permutation Calculator

A permutation counts ordered arrangements (ABC is different from BCA); a combination counts unordered selections (ABC and BCA are the same group). Permutations are always ≥ combinations for the same n and r.

P(n,r) = n! ÷ (n−r)!, the number of ways to arrange r items chosen from n distinct items, where order matters.

C(n,r) = n! ÷ (r! × (n−r)!), which equals P(n,r) ÷ r!. Order doesn't matter, so it's a smaller number than the equivalent permutation count.

When items can be reused, like a 4-digit PIN (10^4 possibilities) or a password where letters can repeat. That's simply n^r.