1998 Pascal Problem 23

The numbers 123\,456\,789 and 999\,999\,999 are multiplied. How many of the digits in the final result are 9's?

\textbf{(A)}\ 0\quad \textbf{(B)}\ 1\quad \textbf{(C)}\ 2\quad \textbf{(D)}\ 3\quad \textbf{(E)}\ 17

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.