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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Doubt on Separator Method tagged by: Brent@GMATPrepNow ##### This topic has 7 expert replies and 7 member replies ## Doubt on Separator Method 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 {D} _________________ R A H U L ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12655 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 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 (= 8 ways) Cheers, Brent Aside: For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=775 _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Upvotes: 448 Target GMAT Score: 750 GMAT Score: 650 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 GMAT Instructor Joined 08 Dec 2008 Posted: 12655 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 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: - http://www.beatthegmat.com/mba/2013/07/31/combinations-and-non-combinations-part-i - http://www.beatthegmat.com/mba/2013/08/28/combinations-and-non-combinations-part-ii - http://www.beatthegmat.com/mba/2013/09/27/does-order-matter-combinations-and-non-combinations-part-iii Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15103 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 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: http://www.beatthegmat.com/inserting-stick-or-seperator-rule-t267423.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 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Upvotes: 448 Target GMAT Score: 750 GMAT Score: 650 Thanks Brent & Mitch for clarifying the doubt... _________________ R A H U L Master | Next Rank: 500 Posts Joined 23 Jun 2013 Posted: 283 messages Followed by: 25 members Upvotes: 97 Test Date: August 12, 2013 GMAT Score: 750 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 {D} 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-attempt-750-in-2-months-t268332.html#688494 Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 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 (= 8 ways) Cheers, Brent Aside: For more information about the FCP, watch our free video: http://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 Elite Legendary Member Joined 23 Jun 2013 Posted: 10071 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 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 Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 But prompt also says "such a way that some of the offices can be empty " ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10071 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 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 Newbie | Next Rank: 10 Posts Joined 08 Aug 2016 Posted: 2 messages [quote="Brent@GMATPrepNow"][quote="theCodeToGMAT"]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 ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 [quote="Hossain"][quote="Brent@GMATPrepNow"] 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

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Newbie | Next Rank: 10 Posts
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[quote="DavidG@VeritasPrep"][quote="Hossain"]
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.

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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? )

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

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