AMC 8 2011 Problem 12
AMC8 2011 年第 12 题
概率★★★☆☆
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
Angie，Bridget，Carlos 和 Diego 随机围着一张方桌坐下，一人坐一边。那么 Angie 和 Carlos 面对面坐着的概率是多少？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
If we designate a person to be on a certain side, then all placements of the other people can be considered unique. WLOG, assign Angie to be on the side. There are then 3!=6 total seating arrangements. If Carlos is across from Angie, there are only 2!=2 ways to fill the remaining two seats. Then the probability Angie and Carlos are seated opposite each other is .
If we seat Angie first, there would be only one out of three ways Carlos can sit across from Angie. So the final answer is Three people can be seated opposite of Angie (Bridget, Carlos, or Diego). Only one of these is Carlos. Thus, the answer is . - @scthecool
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