1-0. The number 111123445678 is written on the board, and several digits (not all) need to be erased to get a number that is a multiple of 5. In how many ways can this be done?
Answer: 60

Solution. The digits 6, 7, and 8 must be crossed out, and 5 must be kept (otherwise, the number will not be divisible by 5). Each digit before the five can be crossed out or not. There are two options for each of the digits 2 and 3 (cross out or not), three options for the digit 4 (do not cross out, cross out one, or cross out both), and five options for the ones (do not cross out any, cross out one, two, three, or all four). The deletions of different digits are independent events, so the obtained numbers should be multiplied: $5 \cdot 3 \cdot 2 \cdot 2=60$.