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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
A certain company has 18 equally qualified applicants for 4 open posit
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24 Feb 2023, 08:34
24 Feb 2023, 08:34
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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
(A) 18
(B) 72
(C) 180
(D) 1,260
(E) 3,060
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: A certain company has 18 equally qualified applicants for 4 open posit
[#permalink]
27 Feb 2023, 02:13
27 Feb 2023, 02:13
1
Expert Reply
This is a combination problem, which involves choosing a certain number of objects from a set without regard to the order in which they are chosen. The formula for combinations is:
n C r = n! / r!(n - r)!
where n is the total number of objects, and r is the number of objects being chosen.
In this problem, there are 18 applicants and 4 open positions, and we want to know how many different groups of 4 applicants can be chosen. So we have:
n = 18
r = 4
Using the combination formula, we get:
18 C 4 = 18! / 4!(18 - 4)!
= (18 x 17 x 16 x 15) / (4 x 3 x 2 x 1)
= 3060
Therefore, there are 3,060 different groups of 4 applicants that can be chosen by the company to fill the positions if the order of selection does not matter. The answer is (E).
n C r = n! / r!(n - r)!
where n is the total number of objects, and r is the number of objects being chosen.
In this problem, there are 18 applicants and 4 open positions, and we want to know how many different groups of 4 applicants can be chosen. So we have:
n = 18
r = 4
Using the combination formula, we get:
18 C 4 = 18! / 4!(18 - 4)!
= (18 x 17 x 16 x 15) / (4 x 3 x 2 x 1)
= 3060
Therefore, there are 3,060 different groups of 4 applicants that can be chosen by the company to fill the positions if the order of selection does not matter. The answer is (E).
gmatclubot
Re: A certain company has 18 equally qualified applicants for 4 open posit [#permalink]
27 Feb 2023, 02:13
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