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?

A) 18 B) 72 C) 180 D) 1,260 E) 3,060

Answer 1

Answer: E) 3,060

Explanation:

Given : The total number of equally qualified applicants = 18

The number of positions = 4

If order of selection does not matter , then we use combinations.

So , the number of different groups of 4 applicants can be chosen by the company to fill the positions =
`^(18)C_4=(18!)/(4!(18-4)!)`

[ ∵
`^nC_r=(n!)/(r!(n-r)!)`]

`=(18*16*17*15*14!)/((24)14!)`

`=3060`

Therefore , the number of different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter = 3,060.

Therefore , the correct answer is E) 3,060