Permutations with Repetition Calculator

About this calculator

When order matters and repeated choices are allowed, the count of possible arrangements of length r drawn from n items is simply n^r — each of the r positions independently has n options, so the counts multiply. This is different from permutations without repetition (n!/(n−r)!), where each item can only be used once.

It's the exact math behind a 4-digit PIN (10^4 = 10,000 combinations), a password built from a fixed character set, or a padlock with multiple dials — anywhere the same symbol can be reused in different positions. Security analysts use n^r directly to estimate how many attempts a brute-force attack would need against a given PIN or password length.