2000 Pascal Problem 24

There are seven points on a piece of paper. Exactly four of these points are on a straight line. No other line contains more than two of these points. Three of these seven points are selected to form the vertices of a triangle. How many triangles are possible?

\textbf{(A)}\ 18\quad \textbf{(B)}\ 28\quad \textbf{(C)}\ 30\quad \textbf{(D)}\ 31\quad \textbf{(E)}\ 33

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.