7. How many two-digit numbers are there in which: a) there is at least one digit 3; b) the number of tens is less than the number of units?
7. a) The digit 3 starts 10 numbers (from 30 to 39 inclusive), and ends in this digit in a total of 9 numbers, but the number 33 has already been counted, so there are 8 such numbers left. Therefore, the total number of such numbers is $10+8=18$.

b) From 10 to 20, there are 8 such numbers (12, 13, ..., 19), from 21 to 30 there are 7, from 31 to 40 there are 6, and so on, from 81 to 90 there is one number 89. Therefore, the total number of such numbers is $8+7+6+\ldots+2+1=9 \cdot 4=36$.