Question

三个姓名不同的学生排成一列。从前到后按字母顺序排列的概率是多少？

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

$\dfrac{1}{12}$

$\dfrac{1}{9}$

$\dfrac{1}{6}$

$\dfrac{1}{3}$

$\dfrac{2}{3}$

队首有 $3$ 种选择，中间有 $2$ 种选择。

最后剩 $1$ 种选择，所以共有 $3 \cdot 2 \cdot 1 = 6$ 种排列。

其中只有一种按字母顺序排列，所以概率为 $\dfrac{1}{6}$ 。

所以正确答案是 C。

There are $3$ options for the person in front. Then, there are $2$ options for the person in the middle.

This leaves $1$ choice for the person at the end. There are $3 \cdot 2 \cdot 1 = 6$ ways for the people to line up.

Only one of these lines is correct, and the probability it occurs is $\dfrac{1}{6}.$

Thus, C is the correct answer.