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 th prize and the winner bowls #3 in another game. The loser of this game receives th prize and the winner bowls #2. The loser of this game receives 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?
Solution
We have choices for who wins the first game, and that uniquely determines place. Then there are choices for a next game and that uniquely determines place, followed by choices for the next game that uniquely determines place. Finally, there are choices for the last game, which uniquely determines both and places, since the winner is and the loser is . Thus the number of possible orders is , which is .
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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