Four-letter passwords

Problem

How many $4$-character passwords can be formed with the $26$ lower-case letters of the English alphabet?

Solution

The order matters and each letter may repeat: these are arrangements with repetition of $26$ objects in groups of $4$, that is $n^k = 26^4$. Each position has $26$ independent choices: $26^4 = \boxed{456\,976}$

Links

Topics: Probabilita
Concepts: Disposizioni con ripetizione
Methods: Disposizioni ripetizione
Skills: Calcolo combinatorio
Exercise type: Problema combinatorio