If zip codes have $5$ digits and each digit can be $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$, then how many zip codes are there with exactly $n$ odd digits?
The way I see it, there are $10^5$ possibilities total.
For exactly one odd digit, we need one odd digit and four even digits. Which makes the answer $5^5$ but this can't be right, because according to this same logic $5^5$ is the answer for all other $n$'s too!
EDIT: And this also doesn't take position into account. I.e. 52222 is not the same as 25222 and etc.