Three students, with different names, line up single file.  What is the probability that they are in alphabetical order from front-to-back?
$\text{(A)}\ \dfrac{1}{12} \qquad \text{(B)}\ \dfrac{1}{9} \qquad \text{(C)}\ \dfrac{1}{6} \qquad \text{(D)}\ \dfrac{1}{3} \qquad \text{(E)}\ \dfrac{2}{3}$
There are $3$ ways to pick the first student, $2$ ways to pick the second student, and $1$ way to pick the last student, for a total of $3! = 3\times2\times1 = 6$ ways to line the students up.
Only $1$ of those ways is alphabetical.  Thus, the probability is $\frac{1}{6}$ or $\boxed{C}$