AMC8 1997

AMC8 1997 · Q9

AMC8 1997 · Q9. It mainly tests Combinations, Probability (basic).

Three students, with different names, line up single file. What is the probability that they are in alphabetical order from front-to-back?

三个学生，名字不同，排成一列单队。从前到后按字母顺序排列的概率是多少？

(A) $\frac{1}{12}$ $\frac{1}{12}$

(B) $\frac{1}{9}$ $\frac{1}{9}$

(D) $\frac{1}{3}$ $\frac{1}{3}$

(E) $\frac{2}{3}$ $\frac{2}{3}$

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (B): Walter is gone from 7:30 AM until 4:00 PM, a total of 8 hours and 30 minutes. He is in class for $6(50\ \text{min.})=300\ \text{min.}$ or 5 hrs., at lunch for $\frac{1}{2}$ hr., and has 2 hours additional time. His total time at school is 7 hrs. and 30 min., so he was on the bus for 1 hour or 60 minutes.

答案（B）：Walter 从上午 7:30 到下午 4:00 不在家，一共 8 小时 30 分钟。他上课时间为 $6(50\ \text{分钟})=300\ \text{分钟}$，即 5 小时；午餐时间为 $\frac{1}{2}$ 小时；另外还有 2 小时的额外时间。他在学校的总时间是 7 小时 30 分钟，所以他在公交车上的时间是 1 小时，即 60 分钟。

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