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To fill a number of vacancies, an employer must hire 3 programmers fro

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To fill a number of vacancies, an employer must hire 3 programmers fro [#permalink]

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To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants and 2 managers from among 4 applicants. What is the total number of ways in which she can make her selection?

(A) 1,490
(B) 132
(C) 120
(D) 60
(E) 23
[Reveal] Spoiler: OA

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Re: To fill a number of vacancies, an employer must hire 3 programmers fro [#permalink]

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New post 14 Mar 2017, 04:15
To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants and 2 managers from among 4 applicants. What is the total number of ways in which she can make her selection?

This is a combination problem that can be accomplished in two stages:

1. We find the possible combinations of 3 programmers among a pool of 6 ---> 6C3 = 20
2. We find the possible combinations of 2 managers among a pool of 4 -------> 4C2 = 6
3. Finally, by the fundamental counting principle, we multiply together in order to find the total possible combinations --> 20*6 = 120
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Re: To fill a number of vacancies, an employer must hire 3 programmers fro [#permalink]

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SajjadAhmad wrote:
To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants and 2 managers from among 4 applicants. What is the total number of ways in which she can make her selection?

(A) 1,490
(B) 132
(C) 120
(D) 60
(E) 23


This is a combination problem since the order of selecting the applicants for each job title does not matter.

3 programmers from 6 applicants can be hired in 6C3 ways:

6C3 = 6!/3!(6-3)! = (6 x 5 x 4)/3! = (6 x 5 x 4)/(3 x 2 x 1) = 20

2 managers from 4 applicants can be hired in 4C2 ways:

4C2 = 4!/2!(4-2)! = (4 x 3)/2! = (4 x 3)/(2 x 1) = 6

Thus, the total number of ways in which she can make her selection is 20 x 6 = 120.

Answer: C
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Re: To fill a number of vacancies, an employer must hire 3 programmers fro [#permalink]

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New post 17 Mar 2017, 01:59
ways of selecting 3 programmer from 6 = 6C3 = 20
ways of selecting 2 managers from 4 = 4C2 = 6

therefore total ways = 20 * 6 = 120
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Re: To fill a number of vacancies, an employer must hire 3 programmers fro [#permalink]

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New post 18 Mar 2017, 22:43
For programmers=6c3=20
For managers=4c2=6
Therefore total number of ways=20*6=120
option"c"
Re: To fill a number of vacancies, an employer must hire 3 programmers fro   [#permalink] 18 Mar 2017, 22:43
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