Question

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

$\dfrac{1}{12}$

$\dfrac{1}{9}$

$\dfrac{1}{6}$

$\dfrac{1}{3}$

$\dfrac{2}{3}$

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.