Last visit was: 27 Apr 2026, 05:56 It is currently 27 Apr 2026, 05:56
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
azamaka
avatar
Joined: 10 Jun 2014
Last visit: 03 Feb 2020
Posts: 17
Own Kudos:
113
 [9]
Given Kudos: 119
Posts: 17
Kudos: 113
 [9]
An employer has 6 applicants for a programming position 10 Sep 2016, 07:10
1
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

83% (01:08) correct 17% (01:34) wrong based on 231 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
C
User avatar
abhimahna
User avatar
Board of Directors
Joined: 18 Jul 2015
Last visit: 06 Jul 2024
Posts: 3,481
Own Kudos:
5,779
 [1]
Given Kudos: 346
Status:Emory Goizueta Alum
Products:
My Reviews
Expert
Expert reply
Posts: 3,481
Kudos: 5,779
 [1]
An employer has 6 applicants for a programming position 10 Sep 2016, 07:21
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
azamaka
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
Show more

6C3 * 4C2 = 120. Answer C.
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,474
 [1]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,474
 [1]
An employer has 6 applicants for a programming position 19 Nov 2017, 14:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
azamaka
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
Show more

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: https://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)

Answer: C

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

RELATED VIDEOS




User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,717
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,717
 [1]
An employer has 6 applicants for a programming position 22 Nov 2017, 12:25
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
azamaka
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
Show more

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.

Answer: C
avatar
mtoti1
avatar
Joined: 04 Feb 2019
Last visit: 29 May 2020
Posts: 1
Given Kudos: 25
Posts: 1
Kudos: 0
An employer has 6 applicants for a programming position 05 Feb 2019, 18:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why do we do 20x6 and not 20 + 6?
User avatar
MartyTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 24 Nov 2014
Last visit: 11 Aug 2023
Posts: 3,471
Own Kudos:
5,645
 [1]
Given Kudos: 1,430
Status:Chief Curriculum and Content Architect
Affiliations: Target Test Prep
GMAT 1: 800 Q51 V51
Expert
Expert reply
GMAT 1: 800 Q51 V51
Posts: 3,471
Kudos: 5,645
 [1]
An employer has 6 applicants for a programming position 05 Feb 2019, 19:27
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
mtoti1
Why do we do 20x6 and not 20 + 6?
Show more
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.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,988
Own Kudos:
1,118
Posts: 38,988
Kudos: 1,118
An employer has 6 applicants for a programming position 04 Dec 2023, 02:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109928 posts
Krunaal
Tuck School Moderator
852 posts