Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 May 2017, 15:42

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain company assigns employees to offices in such a way

Author Message
TAGS:

### Hide Tags

Manager
Joined: 22 Jul 2009
Posts: 196
Location: Manchester UK
Followers: 3

Kudos [?]: 446 [2] , given: 6

A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

08 Jan 2010, 14:18
2
KUDOS
16
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:02) correct 44% (01:18) wrong based on 387 sessions

### HideShow timer Statistics

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. 5
B. 6
C. 7
D. 8
E. 9
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105765 [4] , given: 11581

### Show Tags

08 Jan 2010, 16:58
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
sagarsabnis 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. 5
B. 6
C. 7
D. 8
E. 9
[Reveal] Spoiler:
D

Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2=2^3=8.

_________________
Manager
Joined: 08 Sep 2010
Posts: 227
Location: India
WE 1: 6 Year, Telecom(GSM)
Followers: 4

Kudos [?]: 280 [4] , given: 21

Re: A certain company employee [#permalink]

### Show Tags

25 Oct 2010, 04:26
4
KUDOS
2
This post was
BOOKMARKED
Two offices can be filled in two ways, when all the three employee will be in same room or when two employee in one room and one in other room.

when all the three employee will be in same = 3C3 * 2! =2 (2!, because any of the room can be taken)

when two employee in one room and one in other room. = 3C2 * 1C1 * 2! = 6

Hence total ways = 6+2

Consider KUDOS if it is helpful to u.

Last edited by ankitranjan on 25 Oct 2010, 04:43, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105765 [3] , given: 11581

### Show Tags

09 Jan 2010, 04:25
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
sagarsabnis wrote:
i am still not able to understand. Can you please explain in detail?

also please tell me where i went wrong.This was my logic.

No. of people
office 1: 0|0|0|1|1|1|2|2|3
office 2: 1|2|3|0|1|2|0|1|0

this gives me 9 possible combination

First of all you should assign ALL 3 employees to either of the offices. You can have the following scenarios:

No. of people
***********A|B|C|D|
office 1: 0|1|2|3|
office 2: 3|2|1|0|

In scenario (A) and (D) there is only one way to assign three people. But in (B) and (C) there will be 3 cases in each:

Let's say there are 3 employees: Tom, Mary and Kate. In (B): Tom can be in office #1 and Mary/Kate in #2 OR Mary can be in #1 and Tom/Kate in #2 OR Kate in #1 and Tom/Mary in #2. Total 3 cases for (B). The same for (C). (A)+(B)+(C)+(D)=1+3+3+1=8.

The way I solved this was different:

Each of the three employees, Tom, Mary and Kate, has two choices office #1 or office #2. Hence total # of combinations (assignments) is 2*2*2=2^3=8.

Hope it's clear.
_________________
Senior Manager
Joined: 29 Sep 2009
Posts: 393
GMAT 1: 690 Q47 V38
Followers: 2

Kudos [?]: 38 [2] , given: 5

### Show Tags

21 Nov 2010, 07:12
2
KUDOS
3
This post was
BOOKMARKED
The best way to remember this is :
(Decisions) ^ (Players)
For this problem - 2 decisions , 3 players : 2^3=8
Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105765 [2] , given: 11581

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

07 Jul 2013, 01:13
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
Maxirosario2012 wrote:
Thank you. Then, if the company assigns employees to offices in such a way that if the offices can not be empty and more than one employee can be assigned to an office. And we have 5 employees and 3 rooms, the answer would be:

120?
I mean, 5!

No. It would be 3^5 minus restriction.

For example, for 5 employees and 2 offices it would be 2^5 - 2 ({5-0} and {0-5}).
_________________
Current Student
Joined: 02 Apr 2012
Posts: 77
Location: United States (VA)
Concentration: Entrepreneurship, Finance
GMAT 1: 680 Q49 V34
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 55 [1] , given: 155

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

06 Jul 2013, 17:59
1
KUDOS
Thank you. Then, if the company assigns employees to offices in such a way that if the offices can not be empty and more than one employee can be assigned to an office. And we have 5 employees and 3 rooms, the answer would be:

120?
I mean, 5!
_________________

Encourage cooperation! If this post was very useful, kudos are welcome
"It is our attitude at the beginning of a difficult task which, more than anything else, will affect It's successful outcome" William James

Manager
Joined: 22 Jul 2009
Posts: 196
Location: Manchester UK
Followers: 3

Kudos [?]: 446 [0], given: 6

### Show Tags

09 Jan 2010, 03:27
i am still not able to understand. Can you please explain in detail?

also please tell me where i went wrong.This was my logic.

No. of people
office 1: 0|0|0|1|1|1|2|2|3
office 2: 1|2|3|0|1|2|0|1|0

this gives me 9 possible combination
Manager
Joined: 16 Oct 2010
Posts: 85
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 700 Q49 V35
WE: Information Technology (Investment Banking)
Followers: 0

Kudos [?]: 65 [0], given: 3

Re: A certain company employee [#permalink]

### Show Tags

25 Oct 2010, 04:38
monirjewel 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) 5
B) 6
C) 7
D) 8
E) 9

Every employee has got the possibilit of getting assigned to any of the two offices.
Hence total possibilities = 2^3 = 8
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7368
Location: Pune, India
Followers: 2281

Kudos [?]: 15071 [0], given: 224

### Show Tags

17 Nov 2010, 08:56
Expert's post
1
This post was
BOOKMARKED
SoniaSaini 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. 5
B. 6
C. 7
D. 8
E. 9

For each one of the 3 employees, there are two choices. He can be allotted to any one of the two offices. Hence total number ways will be 2 * 2* 2 = 8 ways
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

SVP
Joined: 16 Nov 2010
Posts: 1666
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 34

Kudos [?]: 533 [0], given: 36

### Show Tags

01 Oct 2012, 13:13
Current Student
Joined: 02 Apr 2012
Posts: 77
Location: United States (VA)
Concentration: Entrepreneurship, Finance
GMAT 1: 680 Q49 V34
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 55 [0], given: 155

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

07 Jul 2013, 13:35
Thank you Bunuel!
I have difficulties learning combinations, this is my weakest area in the GMAT. I am planning to practice all the combinations problems in the forum.
Regarding the problem that I have posted before, I think that you mean:

$$3^5$$ - the combinations in which zero is an element in the set and it cannot be zero in any of the slots, with the restrictions that the 3 elements must sum up 5):
{(005),(014),(023),(032),(041) ; (050)(140),(230),(320),(410) ; (500),(104),(203),(302),(401)}

243 - 15 = 228

I tried to apply combinatorics formulas to this problem (because writing that set is very time consuming) but I could not figure it out.
Translating the problem:
I need to find the number of combinations of three digits in which at least one of the digits is "0", the sum of those three digits is 5 and the digits range from 0 to 5 (six elements).
Then, substract this number from $$3^5$$
_________________

Encourage cooperation! If this post was very useful, kudos are welcome
"It is our attitude at the beginning of a difficult task which, more than anything else, will affect It's successful outcome" William James

Current Student
Joined: 02 Apr 2012
Posts: 77
Location: United States (VA)
Concentration: Entrepreneurship, Finance
GMAT 1: 680 Q49 V34
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 55 [0], given: 155

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

10 Jul 2013, 12:40
Applying combinations I think would be in this way:
$$C^4_1 * C^2_1 = 4*2 = 8$$
_________________

Encourage cooperation! If this post was very useful, kudos are welcome
"It is our attitude at the beginning of a difficult task which, more than anything else, will affect It's successful outcome" William James

Manager
Joined: 04 Dec 2011
Posts: 80
Schools: Smith '16 (I)
Followers: 0

Kudos [?]: 25 [0], given: 13

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

31 Aug 2013, 07:47
ok, can someone tell me what's wrong with my thinking..
1st office can have any 3 employees.. therefore 3 options,
2nd office can also have any of 3 employees hence again 3 options
so it should be 3*3=9

i think the logic is similar to the way Bunuel did..the only difference is in that case we had 2 choices for each employee therefore it was 2*2*2=8.. but why is the answer different in both cases?
_________________

Life is very similar to a boxing ring.
Defeat is not final when you fall down…
It is final when you refuse to get up and fight back!

1 Kudos = 1 thanks
Nikhil

Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105765 [0], given: 11581

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

03 Sep 2013, 06:42
nikhil007 wrote:
ok, can someone tell me what's wrong with my thinking..
1st office can have any 3 employees.. therefore 3 options,
2nd office can also have any of 3 employees hence again 3 options
so it should be 3*3=9

i think the logic is similar to the way Bunuel did..the only difference is in that case we had 2 choices for each employee therefore it was 2*2*2=8.. but why is the answer different in both cases?

We are distributing employees to the offices not vise-versa.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15378
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

15 Sep 2014, 19:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15378
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

18 Apr 2016, 12:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 10 Apr 2016
Posts: 56
Concentration: Strategy, Entrepreneurship
GMAT 1: 520 Q29 V30
GPA: 3.01
Followers: 0

Kudos [?]: 5 [0], given: 7

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

18 Apr 2016, 12:28
Three people that can go in either office 1 or 2
So 2^3 =8

Important is to see that you are not distributing offices to people. That would be 3^2 instead of 2^3
_________________

Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.

Director
Joined: 07 Dec 2014
Posts: 666
Followers: 3

Kudos [?]: 136 [0], given: 3

A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

18 Apr 2016, 15:46
with 2 offices and 3 employees,
there are 3 ways to have one's own office,
3 ways to share an office with one other, and
2 ways to share an office with two others, or
8 ways total
Attachments

office.jpg [ 34.22 KiB | Viewed 4251 times ]

Intern
Joined: 24 Jun 2016
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: A certain company assigns employees to offices in such a way [#permalink]

### Show Tags

08 Aug 2016, 10:32
For 2 employees in 1 office and the other alone: it should be 3 C 1 x 2 (since we only have to choose 1 out of three who will be alone) and then multiply by 2 since there are two offices?
Re: A certain company assigns employees to offices in such a way   [#permalink] 08 Aug 2016, 10:32

Go to page    1   2    Next  [ 25 posts ]

Similar topics Replies Last post
Similar
Topics:
15 Of 5 employees, 3 are to be assigned an office and 2 are to 12 06 Apr 2017, 09:35
5 There are 50 employees in the office of ABC Company. Of 10 26 Feb 2015, 19:11
9 Of the 800 employees in a certain company, 70% have serviced 10 12 Nov 2016, 01:00
At a certain company, each employee has a salary grade s 6 11 Feb 2013, 09:37
21 A certain company assigns employees to offices in such a way 10 26 Feb 2012, 17:29
Display posts from previous: Sort by