8-character passwords

Statement

How many 8-character passwords can be formed using lowercase letters of the English alphabet, if each character can be any letter?

Solution

Numbered slips (the positions are distinguishable and the order counts) with repetition (each letter can be reused): these are arrangements with repetition of $26$ symbols in $8$ places. $26^8 = \boxed{208\,827\,064\,576}$

Links

Topics: Combinatorics
Concepts: Arrangements
Methods: Arrangements with repetition
Skills: Combinatorial calculus
Exercise type: Combinatorial problem