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

1 Answer
reudhreghs · Geoff K.
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 xx 3 xx 2 xx 1 = 24# possibilities overall.

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

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