- There are 248 students in a class. In how many ways is it possible to pair the students, in two and two in a pair ?
Here is the basic idea.
Use the first person on the class roll, how many ways can you pick his or her partner?
Repeat the idea again and again until done.
$\displaystyle \prod\limits_{k = 0}^{123} {(247 - 2k)} $ that is the same as $\displaystyle \frac{248!}{2^{124}(124!)}$