1998 Gauss 8 Problem 17

In a ring toss game at a carnival, three rings are tossed over any of three pegs. A ring over peg A is worth *one* point, over peg B *three* points and over peg C *five* points. If all three rings land on pegs, how many different point totals are possible? (It is possible to have more than one ring on a peg.)

\textbf{(A)}\ 12\quad \textbf{(B)}\ 7\quad \textbf{(C)}\ 10\quad \textbf{(D)}\ 13\quad \textbf{(E)}\ 6

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 Gauss contests here.