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Problem 651

AMC 10/12, early questions

Combinatorics Difficulty 3.0 Find the answer CEMC Gauss (Grade 8) · Canada · 1998

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.) (A) $12$ (B) $7$ (C) $10$ (D) $13$ (E) $6$

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