Question

In how many ways can 4 students from a group of 9 be seated in a row of 4 chairs?

Answer 1

If seating 1, 2, 3, 4 is different 4, 3, 2, 1, then there are 3024 ways to seat the students. if 1, 2, 3, 4 is not different than 4, 3, 2, 1, then there are 126 ways.

Explanation:

It's unclear from the question if having persons 1, 2, 3, 4 and 4, 3, 2, 1 in the chairs is the same (so how many ways can groups be seated) or different. I think it reads as being different and so will show that first (but will do the other way too just in case!)

If 1, 2, 3, 4 is different from 4, 3, 2, 1, then we're dealing with a permutation and that can be found this way:

`P_(9,4)=(9!)/((9-4)!)=(9!)/(5!)` and we can evaluate it:

`(9xx8xx7xx6xx5!)/(5!)=3024`

If 1, 2, 3, 4 is not different from 4, 3, 2, 1, then we're dealing with a combination and that can be found this way:

`P_(9,4)=(9!)/(4!(9-4)!)=(9!)/(4!5!)` and we can evaluate it:

`(cancel9^3xxcancel8xx7xx6xxcancel(5!))/(cancel4xxcancel3xxcancel2xxcancel(5!))=3xx7xx6=126`