Question

How many ways can 4 students be arranged in a row?

Answer 1

`4! = 4 xx 3 xx 2 xx 1 = 24` possibilities

Explanation:

Let's say they're going to be sat on chairs, numbered `1,2,3,4`.

To start with, the students are stood off to the side and you have to sit them on the chairs.

For chair `1`, you have `4` students stood off to the side, so there are `4` possibilities for chair `1`.

No matter which student you choose, you will sit a student on the chair and have `3` students left standing. This means that for chair `2`, you have `3` possibilities.

Now again, no matter who you choose, you have `2` students left standing, so there are `2` possibilities for chair `3`.

Now you'll sit the last one down on the last chair - there's only `1` possibility for the last chair.

In probability, when you have certain numbers of possibilities for a certain number of events, you multiply the numbers of possibilities, so you have

`4 xx 3 xx 2 xx 1 = 24` possibilities overall.

This is also known as `4`-factorial, or `4!`.