• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Doubt on Separator Method

This topic has expert replies
User avatar
Legendary Member
Posts: 1556
Joined: 14 Aug 2012
Thanked: 448 times
Followed by:34 members
GMAT Score:650

Doubt on Separator Method

by theCodeToGMAT » Tue Oct 22, 2013 9:58 am
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9


I solved the question and got: 4!/3!1! ==> 4

However the answer is [spoiler]{D}[/spoiler]
R A H U L

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 13600
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1256 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Oct 22, 2013 10:03 am
theCodeToGMAT wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9
Let X, Y and Z be the 3 employees.
Let A and B be the 2 offices.


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

Stage 1: Assign employee X to an office
There two options (office A or office B), so we can complete stage 1 in 2 ways

Stage 2: Assign employee Y to an office
There two options (office A or office B), so we can complete stage 2 in 2 ways

Stage 3: Assign employee Z to an office
There two options (office A or office B), so we can complete stage 3 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus assign all employees to offices) in (2)(2)(2) ways ([spoiler]= 8 ways[/spoiler])

Cheers,
Brent

Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775
Brent Hanneson - Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide
Image
Sign up for free Question of the Day emails
And check out all of these free resources

User avatar
Legendary Member
Posts: 1556
Joined: 14 Aug 2012
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Tue Oct 22, 2013 10:27 am
Oh, ok..

I was trying to solve the question using Separator method..

By distributing "3" employees between 2 offices..

So, one separator = (3+1)!/3! = 4.

Thanks Brent!!!
R A H U L

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 13600
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1256 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Oct 22, 2013 10:54 am
theCodeToGMAT wrote:Oh, ok..

I was trying to solve the question using Separator method..

By distributing "3" employees between 2 offices..

So, one separator = (3+1)!/3! = 4.

Thanks Brent!!!
The only issue with your method is that it does not treat the offices as distinct.
That is, it treats X and Y in office A and Z in office B as the same as X and Y in office B and Z in office A.
So, account for this, we just need to double your answer.

Having said that, I always begin every counting question by asking, "Can I take the required task and break it into individual stages?" If the answer is yes, I may be able to use the Fundamental Counting Principle (FCP) to solve the question.

More on this strategy here:
- https://www.beatthegmat.com/mba/2013/07/ ... ons-part-i
- https://www.beatthegmat.com/mba/2013/08/ ... ns-part-ii
- https://www.beatthegmat.com/mba/2013/09/ ... s-part-iii

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide
Image
Sign up for free Question of the Day emails
And check out all of these free resources

User avatar
GMAT Instructor
Posts: 15495
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1879 members
GMAT Score:790

by GMATGuruNY » Tue Oct 22, 2013 1:32 pm
theCodeToGMAT wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9
The SEPARATOR method is great for counting the number of ways to distribute n IDENTICAL OBJECTS among r DISTINCT BOXES.
An example:
https://www.beatthegmat.com/inserting-st ... 67423.html
Here, the objects being distributed -- the employees -- are NOT identical.
Thus, the separator method is inappropriate.
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

User avatar
Legendary Member
Posts: 1556
Joined: 14 Aug 2012
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Tue Oct 22, 2013 5:23 pm
Thanks Brent & Mitch for clarifying the doubt...
R A H U L

User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: 23 Jun 2013
Location: Bangalore, India
Thanked: 97 times
Followed by:26 members
GMAT Score:750

by ganeshrkamath » Tue Oct 22, 2013 8:24 pm
theCodeToGMAT wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9


I solved the question and got: 4!/3!1! ==> 4

However the answer is [spoiler]{D}[/spoiler]
Each employee can go to any of the 2 offices.
So the total number of combinations = 2*2*2 = 8

Choose D

Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

Legendary Member
Posts: 518
Joined: 12 May 2015
Thanked: 10 times

by nikhilgmat31 » Wed Oct 07, 2015 12:01 am
Brent@GMATPrepNow wrote:
theCodeToGMAT wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9
Let X, Y and Z be the 3 employees.
Let A and B be the 2 offices.


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

Stage 1: Assign employee X to an office
There two options (office A or office B), so we can complete stage 1 in 2 ways

Stage 2: Assign employee Y to an office
There two options (office A or office B), so we can complete stage 2 in 2 ways

Stage 3: Assign employee Z to an office
There two options (office A or office B), so we can complete stage 3 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus assign all employees to offices) in (2)(2)(2) ways ([spoiler]= 8 ways[/spoiler])

Cheers,
Brent

Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775
Hi Brent,

you didn't consider the option of both the offices empty.

so answer should be 2*2*2 +1 = 9

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10333
Joined: 23 Jun 2013
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:500 members
GMAT Score:800

by Rich.C@EMPOWERgmat.com » Wed Oct 07, 2015 8:58 am
Hi nikhilgmat31,

The prompt states that the 3 employees have to be assigned to two different offices, so it is NOT possible that both offices would be empty.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at Rich.C@empowergmat.com
Image

Legendary Member
Posts: 518
Joined: 12 May 2015
Thanked: 10 times

by nikhilgmat31 » Thu Oct 08, 2015 12:00 am
But prompt also says "such a way that some of the offices can be empty "

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10333
Joined: 23 Jun 2013
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:500 members
GMAT Score:800

by Rich.C@EMPOWERgmat.com » Thu Oct 08, 2015 8:53 am
Hi nikhilgmat31,

I agree that the wording of the prompt is 'clunky', but if there are only 2 offices, and each of the 3 employees has to be assigned to one of them, then where would they be assigned if all of the offices were empty? Logically, this doesn't make sense.

The prompt would have been clearer if it had stated "....in such a way that AN office can be empty..." Questions on the Official GMAT are almost always more clearly worded than this prompt.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at Rich.C@empowergmat.com
Image

Newbie | Next Rank: 10 Posts
Posts: 2
Joined: 08 Aug 2016

by Hossain » Mon Aug 08, 2016 7:04 am
Brent@GMATPrepNow wrote:
theCodeToGMAT wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9

Why can't we use counting method? I came up with answer A(4).
We can fill the offices(2) with 3 people in 4 ways as given below:

Office-1:3 and Office-2:0;
Office-1:2 and Office-2:1;
Office-1:1 and Office-2:2;
Office-0:0 and Office-2:3

Please let me know how this one can be done using counting method or we shouldn't.

Junayed Hossain

User avatar
Legendary Member
Posts: 2666
Joined: 14 Jan 2015
Location: Boston, MA
Thanked: 1153 times
Followed by:125 members
GMAT Score:770

by DavidG@VeritasPrep » Mon Aug 08, 2016 7:43 am
Hossain wrote:
Brent@GMATPrepNow wrote:
theCodeToGMAT wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9

Why can't we use counting method? I came up with answer A(4).
We can fill the offices(2) with 3 people in 4 ways as given below:

Office-1:3 and Office-2:0;
Office-1:2 and Office-2:1;
Office-1:1 and Office-2:2;
Office-0:0 and Office-2:3

Please let me know how this one can be done using counting method or we shouldn't.

Junayed Hossain
You're missing a few scenarios because we have to consider which people are in which office. Imagine, for example, that there are three people: A, B, and C. Now let's take your second scenario, in which there are two people in office 1 and one person in office two.This could play out three ways

Office 1: A, B Office 2: C
Office 1: A, C Office 2: B
Office 1: B, C Office 2: A

(Which makes sense. There are three people, so, logically, there are three different ways we can select one of them to be the lonely reject in office 2.)

The same logic would be true for the third scenario in which there is one person in office 1 and two people in office 2.
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

Newbie | Next Rank: 10 Posts
Posts: 2
Joined: 08 Aug 2016

by Hossain » Mon Aug 08, 2016 9:22 am
DavidG@VeritasPrep wrote:
Hossain wrote:
Brent@GMATPrepNow wrote:
theCodeToGMAT wrote:A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9

Why can't we use counting method? I came up with answer A(4).
We can fill the offices(2) with 3 people in 4 ways as given below:

Office-1:3 and Office-2:0;
Office-1:2 and Office-2:1;
Office-1:1 and Office-2:2;
Office-0:0 and Office-2:3

Please let me know how this one can be done using counting method or we shouldn't.

Junayed Hossain
You're missing a few scenarios because we have to consider which people are in which office. Imagine, for example, that there are three people: A, B, and C. Now let's take your second scenario, in which there are two people in office 1 and one person in office two.This could play out three ways

Office 1: A, B Office 2: C
Office 1: A, C Office 2: B
Office 1: B, C Office 2: A

(Which makes sense. There are three people, so, logically, there are three different ways we can select one of them to be the lonely reject in office 2.)

The same logic would be true for the third scenario in which there is one person in office 1 and two people in office 2.

Yes,I got it now,Thanks very much.

GMAT/MBA Expert

GMAT Instructor
Posts: 2630
Joined: 12 Sep 2012
Location: East Bay all the way
Thanked: 625 times
Followed by:117 members
GMAT Score:780

by Matt@VeritasPrep » Fri Aug 19, 2016 2:53 am
This just can't be a question: there are too many ambiguities. (Can an office be empty? Are the offices distinguishable? Heck, are the employees? :D)

Once we've clarified those points, the rest is formulaic, but we have to clarify those points before we can answer.