Question

In how many different ways can 4 students be arranged in a row?

Answer 1

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There are 24 different ways 4 students can be arranged in a row.

Explanation:

`" "`
There are 4 students.

We must find in how many different ways they can be arranged in a row.

Let us make a simple table and understand the process.

We can easily see that for Position.1, all the four students have a choice to occupy.

For Position.2, since one student has already taken Position.1, there will be 3 choices for the remaining three students.

This process continues until all the students have used their choices.

Hence,

we conclude that there are

`color(red)(4*3*2*1 = 4! =24`

different ways 4 students can be arranged in a row,

Hope it helps.

Answer 2

`24`

Explanation:

Let's do a little thought experiment:

We have four chairs arranged in a row. For `color(red)"Student A"`, how many different spaces can they be in?

Well there are four open spaces, so there are four different possibilities.

What about `color(blue)"Student B"`? Well, one space is occupied, so there are three spaces left.

What about our next student, `color(purple)"Student C"`? Two of our spaces are occupied, so we only have two left.

If three spaces are occupied, there's only one left for `color(lime)"Student D"`.

We multiply these probabilities together to get

`color(red)4xxcolor(blue)3xxcolor(purple)2xxcolor(lime)1=24`

Therefore, there are `24` different ways `4` students can be arranged. Notice that this is equal to `4!`.

Hope this helps!