1988 AHSME Problems/Problem 18

Problem

At the end of a professional bowling tournament, the top 5 bowlers have a playoff. First #5 bowls #4. The loser receives $5$ th prize and the winner bowls #3 in another game. The loser of this game receives $4$ th prize and the winner bowls #2. The loser of this game receives $3$ rd prize and the winner bowls #1. The winner of this game gets 1st prize and the loser gets 2nd prize. In how many orders can bowlers #1 through #5 receive the prizes?

$\textbf{(A)}\ 10\qquad \textbf{(B)}\ 16\qquad \textbf{(C)}\ 24\qquad \textbf{(D)}\ 120\qquad \textbf{(E)}\ \text{none of these}$

Solution

1988 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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1988 AHSME Problems/Problem 18

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