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

Oct 24, 2017

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

$4 \times 3 \times 2 \times 1 = 24$ possibilities overall.

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