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An employer has 6 applicants for a programming position

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An employer has 6 applicants for a programming position  [#permalink]

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10 Sep 2016, 07:10
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An employer has 6 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?

a) 1,490
b) 132
c) 120
d) 60
e) 23
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Re: An employer has 6 applicants for a programming position  [#permalink]

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10 Sep 2016, 07:21
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azamaka wrote:
An employer has 6 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?

a) 1,490
b) 132
c) 120
d) 60
e) 23

6C3 * 4C2 = 120. Answer C.
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Re: An employer has 6 applicants for a programming position  [#permalink]

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19 Nov 2017, 14:49
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Top Contributor
azamaka wrote:
An employer has 6 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?

a) 1,490
b) 132
c) 120
d) 60
e) 23

Take the task of selecting employees and break it into stages.

Stage 1: Select 3 programmers to hire
Since the order in which we select the programmers does not matter, we can use combinations.
We can select 3 programmers from 6 programmers in 6C3 ways (20 ways)
So, we can complete stage 1 in 20 ways

If anyone is interested, we have a free video on calculating combinations (like 6C3) in your head: http://www.gmatprepnow.com/module/gmat- ... /video/789

Stage 2: Select 2 managers to hire
Once again, we can use combinations
We can select 2 managers from 4 applicants in 4C2 ways (6 ways)
So, we can complete stage 2 in 6 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 (and thus hire all of the people) in (20)(6) ways (= 120 ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: An employer has 6 applicants for a programming position  [#permalink]

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22 Nov 2017, 12:25
azamaka wrote:
An employer has 6 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?

a) 1,490
b) 132
c) 120
d) 60
e) 23

The programmers can be selected in 6C3 = 6!/3![(6-3)!] = (6 x 5 x 4)/3! = (6 x 5 x 4)/(3 x 2) = 20 ways.

The managers can be selected in 4C2 = 4!/[2!(4-2)!] = (4 x 3)/2! = 6 ways.

Thus, the total number of ways to select the group is 20 x 6 = 120.

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Intern
Joined: 04 Feb 2019
Posts: 1
Re: An employer has 6 applicants for a programming position  [#permalink]

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05 Feb 2019, 18:13
Why do we do 20x6 and not 20 + 6?
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Re: An employer has 6 applicants for a programming position  [#permalink]

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05 Feb 2019, 19:27
mtoti1 wrote:
Why do we do 20x6 and not 20 + 6?

Hi mtoti1.

That's a great question.

We multiply rather than add because we aren't adding the two sets of possible groups together. We are making combinations of the groups in the two sets of possible groups.

To see why we multiply to arrive at the numbers of combinations of possible groups, consider the following.

We can choose combinations of possible groups in the following way.

We first choose one of the 20 possible groups of programmers. Then we choose one of the 6 possible groups of managers.

So, for every group of programmers, we have 6 ways to choose a group of managers.

If we choose group 1 of the 20 possible groups of programmers, we have 6 ways to choose managers. So, we have 6 ways to choose after we choose group 1 of the programmers.

If we choose group 2 of the 20 different groups of programmers, we again have 6 ways to choose managers. So, we have 6 ways to choose after we choose group 2 of the programmers.

If we choose group 3 of the programmers, we have again 6 different ways to choose managers.

We have 20 total ways to choose programmers, and, for each of those, there are 6 different ways to choose managers.

So, once we know that we have 20 ways to choose programmers and 6 ways to choose managers, we can calculate that we have 20 x 6 = 120 ways to choose a group of programmers and then a group of managers.
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Re: An employer has 6 applicants for a programming position   [#permalink] 05 Feb 2019, 19:27
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