There is a problem in which I am obtaining a different answer than my professor. The problem is as follows:
How many integers between $1$ and $1000$ use exactly three digits?
The professor shows the solution as: $9 \cdot 9 \cdot 8=648$, but I have no idea where those numbers are coming from. On the other hand, I say that, excluding $1$ to $99$ and $1000$, there are $900$ integers that use exactly three digits. Can someone please explain which one of us is right and why?