Task 3. Determine the number of:

a) two-digit

b) three-digit numbers

that are written only with even digits.
Solution. a) The tens place can be occupied by 4 digits, which are 2, 4, 6, and 8. The units place can be occupied by 5 digits, which are $0, 2, 4, 6$, and 8. Therefore, there are a total of $4 \cdot 5=20$ two-digit numbers.

b) From the two-digit numbers, three-digit numbers are obtained by appending one of the digits $0, 2, 4, 6$, and 8 to the right of each two-digit number. Therefore, there are $20 \cdot 5=100$ three-digit numbers.