AMC 8 2014 Problem 16
AMC8 2014 年第 16 题
基本计数原理★★★☆☆
The "Middle School Eight" basketball conference has 8 teams. Every season, each team plays every other conference team twice (home and away), and each team also plays 4 games against non-conference opponents. What is the total number of games in a season involving the "Middle School eight" teams?
“中学八队”篮球联盟共有 8 支球队。每一个赛季，篮球联盟内的每支球队都会与联盟内的其他球队进行两场比赛（主客场），联盟内的每支球队也会与非联盟对手进行 4 场比赛。“中学八队”球队在一个赛季中的比赛总数是多少？
- A.60
- B.88
- C.96
- D.144
- E.160
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
Within the conference, there are 8 teams, so there are pairings of teams, and each pair must play two games, for a total of games within the conference. Each team also plays 4 games outside the conference, and there are 8 teams, so there are a total of games outside the conference. Therefore, the total number of games is .
We can also figure out the number of games the 8 teams play within the conference with the formula n(n - 1)/2, which is used for these kind of match questions, where Team A playing Team B is the same as Team B playing Team A. In this formula, n is the number of teams. So we will do (8 X 7 / 2) X 2, as each team plays the other team twice. The 2s cancel out, to yield 8 X 7, which is 56 games. Then, we can just proceed as above to find the number of games the 8 teams play against 4 teams outside the conference, which is 8 X 4 = 32. Summing these values up yields 88, which is answer choice B.
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