AMC8 2005
AMC8 2005 · Q14
AMC8 2005 · Q14. It mainly tests Basic counting (rules of product/sum), Combinations.
The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many conference games are scheduled?
Little Twelve 篮球联盟有两个分区的每个分区有 6 个队。每队与其本分区的其他队各打两次，与另一分区的每队打一次。联盟总共安排了多少场比赛？
(A)
80
80
(B)
96
96
(C)
100
100
(D)
108
108
(E)
192
192
Answer
Correct choice: (B)
正确答案：（B）
Solution
(B) Each team plays 10 games in its own division and 6 games against teams in the other division. So each of the 12 teams plays 16 conference games. Because each game involves two teams, there are $\frac{12\times16}{2}=96$ games scheduled.
(B) 每支球队在本分区进行 10 场比赛，并与另一个分区的球队进行 6 场比赛。因此，12 支球队中每支球队都要打 16 场联盟比赛。由于每场比赛涉及两支球队，所以安排的比赛总数为 $\frac{12\times16}{2}=96$ 场。
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