Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to pre-think assumptions and solve the most challenging questions in less than 2 minutes.
An employer has 6 applicants for a programming position
[#permalink]
Show Tags
10 Sep 2016, 07:10
4
00:00
A
B
C
D
E
Difficulty:
15% (low)
Question Stats:
78% (01:09) correct 22% (01:32) wrong based on 108 sessions
HideShow timer Statistics
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?
Re: An employer has 6 applicants for a programming position
[#permalink]
Show Tags
10 Sep 2016, 07:21
1
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?
Re: An employer has 6 applicants for a programming position
[#permalink]
Show Tags
19 Nov 2017, 14:49
1
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
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)
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
Re: An employer has 6 applicants for a programming position
[#permalink]
Show Tags
22 Nov 2017, 12:25
1
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.
Re: An employer has 6 applicants for a programming position
[#permalink]
Show Tags
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.
_________________