Part (a): How many positive integers are there whose digits strictly increase from left to right? (For example, $28$, $13589$, and $4$ are all such integers. "Strictly" means no two digits can be equal, so $15668$ wouldn't count.)
Part (b): Among the positive integers whose digits strictly increase from left to right, how many have at most one even digit?
I don't know how to start part (a) but for part (b) I think I can just choose 1 of the digits to be even and there are 5 choices (0, 2, 4, 6 ,8), unless the first digit is even, then there is no 0.