Combinatorics: How many numerical strings of length 5 have exactly one even digit?

Question

Attempted solutions:
$5$ placements $\times 5^4$ (leftover digits of even numbers)
$5$ placements $\times 5!$ ( no idea, just trying )
$5$ placements $\times 2^4$ ( because it could either be even or odd)

Well everything up here is wrong.

Answer 1

Your first idea was along the right track: You place one even digit, and then you need $4$ more odd digits. So for those $4$ odd digits, you indeed have $5^4$ possibilities. And yes, there are $5$ placements for that even digit, but you also have $5$ options for what that even digit is. So ...