# Arrange 248 people in pairs

• October 3rd 2012, 06:43 AM
frimanns
Arrange 248 people in pairs
1. 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 ?

• October 3rd 2012, 07:59 AM
Plato
Re: Arrange 248 people in pairs
Quote:

Originally Posted by frimanns
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.
$\prod\limits_{k = 0}^{123} {(247 - 2k)}$ that is the same as $\frac{248!}{2^{124}(124!)}$