1998 Cayley Problem 19

Mr. Anderson has more than 25 students in his class. He has more than 2 but fewer than 10 boys and more than 14 but fewer than 23 girls in his class. How many different class *sizes* would satisfy these conditions?

\textbf{(A)}\ 5\quad \textbf{(B)}\ 6\quad \textbf{(C)}\ 7\quad \textbf{(D)}\ 3\quad \textbf{(E)}\ 4

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 Cayley contests here.