Answer:
3060 ways.
Step-by-step 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.
[tex]^{n} C_{r}=\frac{n!}{(n-r)!\ r!}[/tex]
Number of different groups of 4 applicants can be chosen out of 18 in =
[tex]^{18} C_{4}=\frac{18!}{(18-4)!\ 4!}\\\\ =\frac{18\times17\times16\times15\times14!}{14!\times4!} ,\ 14!\ canceled\ by\ 14! \\\\ =\frac{18\times17\times16\times15\times}{4\times3\times2\times1} \\\\ =\frac{73440}{24}\\ \\ =3060\ ways[/tex]
Therefore, different groups of 4 applicants can be chosen by the company in 3060 ways.
