AMC 8 2004 Problem 5
AMC8 2004 年第 5 题
基本计数原理★★☆☆☆
Ms. Hamilton's eighth-grade class wants to participate in the annual three-person-team basketball tournament. The losing team of each game is eliminated from the tournament. If sixteen teams compete, how many games will be played to determine the winner?
Hamilton 女士八年级的班级想参加一年一度的三人篮球团体赛。每场比赛的败队被淘汰出局。如果有 16 支球队参加比赛，将进行多少场比赛来决定最终的冠军？
- A.4
- B.7
- C.8
- D.15
- E.16
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Note that the winning team will the be the only team that wins all of the games. Therefore, to find the total number of games to determine the winner has a 1:1 correspondence to the number of ways to determine the losers. ( Think of it this way: If you want to select two balls from a bag of 6 balls, it is analogous to selecting the 4 balls that you don't want to select, both are 6 choose 2.). There are 15 losing teams, and since each round is unique, there are 15 total rounds.
There will be 8 games the first round, 4 games the second round, 2 games the third round, and 1 game in the final round, giving us a total of 8+4+2+1=15 games. 15.
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