[ [Decimal numeral system ]  [ Problems with constraints ]

Find the number of five-digit numbers in decimal notation that contain at least one digit 8.
Find the number of all five-digit numbers and five-digit numbers that do not contain the digit 8.

## Solution

There are a total of 90000 five-digit numbers (see the solution to problem 60336). Let's find the number of five-digit numbers that do not contain the digit 8. The first digit of such a number cannot be 0 or 8 - there are 8 options; each of the following four places can be any of the 9 digits, except 8. Therefore, the number of such numbers is $8 \cdot 9^{4}=52488$. Thus, the number of five-digit numbers whose representation contains at least one digit 8 is $90000-52488=37512$.

## Answer

37512 numbers.