Question

There are exactly 20 students currently enrolled in a class. How many different ways are there to pair up the 20 students, so that each student is paired with one other student

Answer 1

Answer:

The students can be paired up in 654,729,075 ways

Step-by-step explanation:

The 20 people can organize themselves in a line. The first and second people can make up a pair, the 2nd and 3rd can do the same. This can be done until all 20 of them have a pair. This will be done in 20! ways

If the two people in a pair swap positions. In mathematics, it is considered as a different arrangement.  This can be done $2^{10} ways$ since there are 10 pairs We will have to divide by this.

If the 10 pairs can swap places with each other, it will form another pair. As a matter of fact, the 10 pairs can swap pairs with each other all they like. This can be done in 10! ways. we will also have to divide by this.

Hence the total number of ways = $\frac{20!}{2^{10}\times 10! } = 654,729,075 ways$