simple counting problem causing confusion (foundamental counting principle)

Question

I'm sorry for the basic question, but I can't figure this out.

Suppose you want to find how many even, non-repeating 3-digit numbers there are. If you choose the last digit to be non-zero, you have $(8)(8)(5) = 320$ possibilities. If you choose the last digit to be zero, you have $(9)(8)(5) = 360$ possibilities. What should I do?

Answer 1

If you choose the last digit to be non-zero ($\{2,4,6,8\}$), we have

$$(8)(8)\color{red}{(4)}$$

If you choose the last digit to be zero $\{0\}$, we have

$$(9)(8)\color{red}{(1)}$$

then sum them up.