## Task A-1.5.

How many four-digit numbers are there that are composed of distinct digits from the set $\{0,1,2,3,4,5\}$ and are divisible by 5?
## First Solution.

Since we are considering numbers divisible by 5, the last digit is 0 or 5.

First, let's count the numbers that end with 0, i.e., those of the form $\overline{a b c 0}$. The digits $a, b$, and $c$ must be different from 0, so $a, b, c \in\{1,2,3,4,5\}$.

The digit $a$ can be chosen in 5 ways, the digit $b$ in 4 ways so that it is different from $a$, and the digit $c$ in 3 ways so that it is different from $a$ and $b$. It follows that there are $5 \cdot 4 \cdot 3=60$ of the observed four-digit numbers that end with 0. We choose from the set $\{0,1,2,3,4\}$, but $a$ must not be 0 (otherwise, the number would not be a four-digit number). The digit $a$ can be chosen in 4 ways.

After that, since $b$ and $c$ can be 0, the digit $b$ can also be chosen in 4 ways, and $c$ in 3 ways. It follows that there are $4 \cdot 4 \cdot 3=48$ of the observed four-digit numbers that end with 5.

In total, there are $60+48=108$ such numbers.