Codes of a combination lock

Text

A combination lock has $4$ wheels, each showing the $8$ digits from $0$ to $7$. How many distinct combinations does it allow?

Solution

Each wheel is set independently by choosing one of $8$ digits; digits may repeat and order matters. These are arrangements with repetition of $8$ elements taken $4$ at a time: $N = 8^4 = \boxed{4096}.$