1998 Pascal Problem 14

The sum of the digits of a five-digit positive integer is 2. (A five-digit integer cannot start with zero.) The number of such integers is

\textbf{(A)}\ 1\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 5

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.