1988 AMC 12 第 18 题
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18.
一项职业保龄球锦标赛结束时，排名前 的选手进行附加赛。首先，编号 与编号 比赛。负者获得第 名奖金，胜者再与编号 比赛。这场比赛的负者获得第 名奖金，胜者再与编号 比赛。这场比赛的负者获得第 名奖金，胜者再与编号 比赛。最后一场的胜者获得第 名奖金，负者获得第 名奖金。编号 到编号 的选手共有多少种获奖名次顺序？
At the end of a professional bowling tournament, the top bowlers have a play-off. First # bowls # The loser receives th prize and the winner bowls # in another game. The loser of this game receives th prize and the winner bowls # The loser of this game receives rd prize and the winner bowls # The winner of this game gets st prize and the loser gets nd prize. In how many orders can bowlers # through # receive the prizes?
以上都不是
none of these
答案：B
小提示：
一共进行四场比赛
Exactly four games are played
大提示：
每一种胜者序列都确定一种不同的获奖名次顺序
Each sequence of winners determines a different prize order
解答：
四场比赛各有两种可能的胜者。四场比赛的结果序列唯一确定五个获奖名次，所以共有 种顺序。
所以正确答案是 B。
Each of the four games has two possible winners. A sequence of four outcomes uniquely determines the five prize positions, so there are orders.
Thus the correct answer is B.
其他年份的第 18 题
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