Question

A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

Answer 1

3060 ways.

Explanation:

Given:

A certain company has 18 equally qualified applicants for 4 open positions.

Question asked:

How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

Solution:

As mentioned that the order is not important, we will apply formula of combination.

`^(n) C_(r)=(n!)/((n-r)!\ r!)`

Number of different groups of 4 applicants can be chosen out of 18 in =

`^(18) C_(4)=(18!)/((18-4)!\ 4!)\\\\ =(18*17*16*15*14!)/(14!*4!) ,\ 14!\ canceled\ by\ 14! \\\\ =(18*17*16*15*)/(4*3*2*1) \\\\ =(73440)/(24)\\ \\ =3060\ ways`

Therefore, different groups of 4 applicants can be chosen by the company in 3060 ways.