GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 10:48

### 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

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 12 Dec 2015
Posts: 8
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

19 Dec 2016, 09:58
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

Do you know how to solve this problem
In how many ways 4 distinct rings can be can be worn in 3 finger? Is it 3^4 or 4^3??
How do you decide it?

So we have some thing called reducing component here. Which ever reduces goes in the exponent. When you select one ring for any of the three fingers, the rings reduced from 4 to 3. So rings are the reducing factor. Hence no of ring = 4 will go on the exponent. There for correct answer is 3^4 and not 4^3

Similarly here Ring= Employees [Beacuase when you choose any employee to fit into any office, the office remains the same but the employee reduces. Hence employee=3 is the reducing factor}
Finger= Office

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

21 Dec 2016, 10:09
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

We need to determine in how many ways the company can assign 3 employees to 2 different offices when some of the offices can be empty and more than one employee can be assigned to an office.

Since there are 3 people and 2 offices, we have 3 options for each office. Thus, the employees can be organized in 2^3 = 8 possible ways.

Alternative solution:

If you have trouble understanding why there should be 2^3 = 8 possible ways to assign 3 employees in 2 different offices, we can list all the possible ways one can assign 3 employees (say A, B and C) to 2 different offices (Office 1 and Office 2).

1) Office 1: A, B, C and Office 2: no one

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

3) Office 1: A, C and Office 2: B

4) Office 1: B, C and Office 2: A

5) Office 1: A and Office 2: B, C

6) Office 1: B and Office 2: A ,C

7) Office 1: C and Office 2: A, B

8) Office 1: no one and Office 2: A, B, and C

As we can see, there are 8 ways to assign 3 employees to 2 different offices.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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

Director
Joined: 17 Dec 2012
Posts: 623
Location: India
A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

27 May 2017, 05:45
Top Contributor
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

Each of the 3 employees has 2 choices is the best explanation.
So we have 2^3 =8 as the answer.
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Intern
Joined: 21 Sep 2016
Posts: 28
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

10 Sep 2017, 05:17
I solved this in another way, though I don't know whether that's a correct one.

Considering there are 2 alternatives:

A) 3 employees to 1 office we'll have: 3C3 * 2 (since there are 2 offices).
B) 2 employees to 1 office we'll have: 3C2 * 2 (since, as above, there are 2 offices).
Intern
Joined: 16 Jul 2011
Posts: 39
Concentration: Marketing, Real Estate
GMAT 1: 550 Q37 V28
GMAT 2: 610 Q43 V31
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

09 Oct 2017, 12:42
VeritasPrepKarishma wrote:
ashiima wrote:
Hi,
I am kind of lost on all probability type qs :/

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

Think in this way:
There is no restriction on the offices i.e. they can be vacant, they can accommodate all 3 employees etc. But there is a restriction on the employees i.e. each one of them must get an office.

Employee 1 can get an office in 2 ways - office A or office B
Employee 2 can get an office in 2 ways - office A or office B
Employee 3 can get an office in 2 ways - office A or office B
All three can be allotted offices in 2*2*2 = 8 ways
This takes care of all cases.

Hi Karishma,
I understood the logic behind it but I always get confused when it comes to...when do we add the choices and when do we multiply the choices. Can you please explain the rationale behind it and also give a simple example?
_________________
"The fool didn't know it was impossible, so he did it."
Manager
Joined: 23 Sep 2016
Posts: 230
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

26 Feb 2018, 04:18
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

IMO is D as we know each employ has 2 choices between offices then e1=2 e2=2 and e3=2 then 2^3=8
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4158
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

13 Mar 2018, 10:51
Top Contributor
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

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)

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

RELATED VIDEOS

_________________
Test confidently with gmatprepnow.com
VP
Joined: 09 Mar 2016
Posts: 1228
A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

01 May 2018, 06:31
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

pushpitkc

here is my solution to this question:

$$3C1 *2C2 = 6*1$$ ( # of ways to choose 1 employee from 3 and # of ways to choose 2 employees from 2)

$$3C2 *1C1 = 3*1$$ ( # of ways to choose 2 employees from 3 and # of ways to choose 1 employees from 1)

$$6+3 = 9$$

if this is purely combinatorics questions why doesnt our approach work please explain
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3305
Location: India
GPA: 3.12
A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

01 May 2018, 11:24
1
Hi dave13

The major mistake that you have made in this problem is the question stem reads
"One of the offices can have zero employees" also - meaning the other office has full capacity.

There are 2 possibilities when the 3 employees are in either rooms.

Now coming to the mistake in your solution
$$3C1 *2C2 = 6*1$$ ( # of ways to choose 1 employee from 3 and # of ways to choose 2 employees from 2)

Here, $$3C1*2C2 = 3*1 = 3$$. This makes the total possibilities 3+3 = 6

Therefore, the number of possibilities including the case that you missed is 2+6 = 8(Option D)

Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got
VP
Joined: 09 Mar 2016
Posts: 1228
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

03 May 2018, 08:48
pushpitkc wrote:
Hi dave13

The major mistake that you have made in this problem is the question stem reads
"One of the offices can have zero employees" also - meaning the other office has full capacity.

There are 2 possibilities when the 3 employees are in either rooms.

Now coming to the mistake in your solution
$$3C1 *2C2 = 6*1$$ ( # of ways to choose 1 employee from 3 and # of ways to choose 2 employees from 2)

Here, $$3C1*2C2 = 3*1 = 3$$. This makes the total possibilities 3+3 = 6

Therefore, the number of possibilities including the case that you missed is 2+6 = 8(Option D)

Hope this helps you!

Hi pushpitkc , many thanks

can you please confirm my solution below is it correct now ?

$$3C1 *2C2 = 3*1 = 3$$ ( # of ways to choose 1 employee from 3 and # of ways to choose 2 employees from 2)

$$3C2 *1C1 = 3*1 =3$$ ( # of ways to choose 2 employees from 3 and # of ways to choose 1 employees from 1)

$$3C3 *0C0 = 3*0 = 0$$ ( # of ways to choose 3 employees from 3 and # of ways to choose 0 employees from 0) (since the question stem reads
"One of the offices can have zero employees")

Total number of ways: $$3+3+0= 6$$
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3305
Location: India
GPA: 3.12
A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

03 May 2018, 10:39
1
dave13 wrote:
pushpitkc wrote:
Hi dave13

The major mistake that you have made in this problem is the question stem reads
"One of the offices can have zero employees" also - meaning the other office has full capacity.

There are 2 possibilities when the 3 employees are in either rooms.

Now coming to the mistake in your solution
$$3C1 *2C2 = 6*1$$ ( # of ways to choose 1 employee from 3 and # of ways to choose 2 employees from 2)

Here, $$3C1*2C2 = 3*1 = 3$$. This makes the total possibilities 3+3 = 6

Therefore, the number of possibilities including the case that you missed is 2+6 = 8(Option D)

Hope this helps you!

Hi pushpitkc , many thanks

can you please confirm my solution below is it correct now ?

$$3C1 *2C2 = 3*1 = 3$$ ( # of ways to choose 1 employee from 3 and # of ways to choose 2 employees from 2)

$$3C2 *1C1 = 3*1 =3$$ ( # of ways to choose 2 employees from 3 and # of ways to choose 1 employees from 1)

$$3C3 *0C0 = 3*0 = 0$$ ( # of ways to choose 3 employees from 3 and # of ways to choose 0 employees from 0) (since the question stem reads
"One of the offices can have zero employees")

Total number of ways: $$3+3+0= 6$$

Hi dave13

I think this is how this problem can be solved using this method

First room - 2 employees, Second room - 1 employee: 3c2*1c1 = 3*1 = 3
First room - 1 employee, Second room - 2 employee: 3c1*2c2 = 3*1 = 3
3 can be placed in either room - 3c3*2 = 1*2 = 2

Total possibilities: 3+3+2 = 8

All three employees have 2 options of being placed in an office - Office 1 or 2.
Therefore, we will have (2)(2)(2) or 8 ways in which the employees can be placed in the office.

Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got
Manager
Joined: 02 Jul 2016
Posts: 134
Location: India
GMAT 1: 650 Q49 V28
GPA: 4
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

13 May 2018, 22:51
Bunuel wrote:
sagarsabnis wrote:
A certain company assigns employees to offices in such a way thatsome 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

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

Hi Bunuel,
thanks for the explanation.
Initially I got confused from the above highlighted line.
And I did 3*3*3 because a person can either select 1 or 2nd or none.

Thanks
Senior Manager
Joined: 10 Apr 2018
Posts: 267
Location: United States (NC)
A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

21 Sep 2018, 17:05
Hi ,
well this problem has provided some information initially to and the question is actually in last part.

HOW CAN YOU ASSIGN 3 people to 2 offices" this is similar like how can you assign 3 rings to 2 fingers or similar on the lines of how can you post 7 letters to 5 different post boxes.

Say we have two spaces ___I____ and ___II_______ and 3 employees (A, B C)

A has two options either space 1 or space 2 So 2 ways
B has two options either space 1 or space 2 So 2 ways
C has two options either space 1 or space 2 So 2 ways

Altogether a has two and b has two and c has two = 2*2*2= 8 Ways.

Now try the letterbox problem and see if you got the concept .

Probus
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
Non-Human User
Joined: 09 Sep 2013
Posts: 13743
Re: A certain company assigns employees to offices in such a way  [#permalink]

### Show Tags

24 Sep 2019, 21:32
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.
_________________
Re: A certain company assigns employees to offices in such a way   [#permalink] 24 Sep 2019, 21:32

Go to page   Previous    1   2   [ 34 posts ]

Display posts from previous: Sort by