Last visit was: 14 Sep 2024, 07:54 It is currently 14 Sep 2024, 07:54
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 22 Jul 2009
Posts: 82
Own Kudos [?]: 2482 [184]
Given Kudos: 6
Location: Manchester UK
Q48  V28
Math Expert
Joined: 02 Sep 2009
Posts: 95503
Own Kudos [?]: 658493 [53]
Given Kudos: 87257
Manager
Joined: 08 Sep 2010
Posts: 112
Own Kudos [?]: 768 [41]
Given Kudos: 21
Location: India
Concentration: Finance
Q49  V19 GMAT 2: 620  Q44  V31
WE 1: 6 Year, Telecom(GSM)
Senior Manager
Joined: 29 Sep 2009
Posts: 335
Own Kudos [?]: 109 [30]
Given Kudos: 5
GMAT 1: 690 Q47 V38
19
Kudos
11
Bookmarks
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: 95503
Own Kudos [?]: 658493 [26]
Given Kudos: 87257
A certain company assigns employees to offices in such a way [#permalink]
14
Kudos
12
Bookmarks
sagarsabnis
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 three employee can be assigned to either of the two offices, meaning that each employee has 2 choices --> 2*2*2=2^3=8.

GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31311 [11]
Given Kudos: 799
Re: A certain company assigns employees to offices in such a way [#permalink]
6
Kudos
5
Bookmarks
Top Contributor
sagarsabnis
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

General Discussion
Manager
Joined: 22 Jul 2009
Posts: 82
Own Kudos [?]: 2482 [0]
Given Kudos: 6
Location: Manchester UK
Q48  V28
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
Tutor
Joined: 16 Oct 2010
Posts: 15302
Own Kudos [?]: 68054 [8]
Given Kudos: 442
Location: Pune, India
4
Kudos
4
Bookmarks
SoniaSaini
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
Tutor
Joined: 16 Oct 2010
Posts: 15302
Own Kudos [?]: 68054 [8]
Given Kudos: 442
Location: Pune, India
6
Kudos
2
Bookmarks
ashiima
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.
Magoosh GMAT Instructor
Joined: 28 Nov 2011
Posts: 296
Own Kudos [?]: 4610 [15]
Given Kudos: 2
13
Kudos
2
Bookmarks
The fastest way to solve this problem is by using the formula, 2^n, where n stands for the number of elements, or, in this case, the number of employees. This formula is derived from adding the number of combinations from

What’s important with this problem is not to treat it as a probability problem. While on the surface it may seem similar to a typical combinations problem, using the combinations formula to solve the problem is cumbersome.

Instead, use the formula, 2^n, where n stands for the number of elements, or, in this case, the number of employees.

This formula is derived from adding the number of combinations whenever you can select any number greater than zero and less than or equal to n. For instance, here we could have chosen any of three employees for the first office. So instead of using 3C0 + 3C1 + 3C2 + 3C3, we can use 2^3.

This formula becomes especially useful for larger numbers. Imagine the question were:

How many ways can 8 employees go in two offices?

(A) 8
(B) 32
(C) 48
(D) 64
(E) 120

Following the method of finding each case would take too much time. By using 2^n, we 2^8 = 64. (D)

Going back to my original point: do not think of this as a typical probability problem, but one that uses the 2^n concept. The problems, while not really a probability problem, employ the 2^n formula.

Positive integer N is the product of three distinct primes. How many factors in N?

Ans: 2^3 – 1 (zero is not a factor so hence we subtract one from 2^n).

A multiple-choice test has five possible answer choices. Any number of answers can be correct. (e.g. A-B-D is possible answer, C-D, or all five). How many different possible answers?

Ans: 2^5 – 1 = 31 You can’t leave question blank (like the empty office) so therefore -1.

By understanding the concept behind a question, instead of grouping a question under one general category, you should be able to solve problems more quickly.
Manager
Joined: 02 Apr 2012
Posts: 51
Own Kudos [?]: 165 [1]
Given Kudos: 155
Location: United States (VA)
Concentration: Entrepreneurship, Finance
GMAT 1: 680 Q49 V34
WE:Consulting (Consulting)
Re: A certain company assigns employees to offices in such a way [#permalink]
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!
Math Expert
Joined: 02 Sep 2009
Posts: 95503
Own Kudos [?]: 658493 [4]
Given Kudos: 87257
Re: A certain company assigns employees to offices in such a way [#permalink]
3
Kudos
1
Bookmarks
Maxirosario2012
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}).
Intern
Joined: 04 Dec 2011
Posts: 48
Own Kudos [?]: 82 [0]
Given Kudos: 13
Schools: Smith '16 (I)
Re: A certain company assigns employees to offices in such a way [#permalink]
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?
Math Expert
Joined: 02 Sep 2009
Posts: 95503
Own Kudos [?]: 658493 [1]
Given Kudos: 87257
Re: A certain company assigns employees to offices in such a way [#permalink]
1
Bookmarks
nikhil007
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.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19460
Own Kudos [?]: 23238 [1]
Given Kudos: 286
Location: United States (CA)
Re: A certain company assigns employees to offices in such a way [#permalink]
1
Kudos
sagarsabnis
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.

Tutor
Joined: 16 Oct 2010
Posts: 15302
Own Kudos [?]: 68054 [3]
Given Kudos: 442
Location: Pune, India
Re: A certain company assigns employees to offices in such a way [#permalink]
3
Kudos
Responding to a pm:
Quote:
4*1*2=8

we have 4 options ( 0,1,2,or 3 employees) for the first office and 1 for the other. Multiply by 2 as we can assign employees to 2nd office first ,in which case 1st office will have only 1 option. Is this reasoning correct?

No, there is a problem in the logic used. There are 4 ways of distributing employees to the 2 offices. The order in which we distribute them in immaterial. So if we have 1 in office 1 and 2 people in office 2, it doesn't matter whether you put the 1 person in first or the 2 people in first. The final distribution is the same hence the logic of multiplying by 2 is nor correct.

Note that when you put 1 person in office 1 and 2 people in office 2, there are 3 distinct ways of doing it since the people are distinct (say A, B and C)
So A in office 1 and B, C in office 2 is different from B in office 1 and A, C in office 2.

So there is 1 way or 0 in office 1 and 3 in office 2.
3 ways of putting 1 in office 1 and 2 in office 2.
3 ways of putting 2 in office 1 and 1 in office 2.
and 1 way of putting 3 in office 1 and 0 in office 2.

That is how you get 1 + 3 + 3 + 1 = 8 cases.
Tutor
Joined: 16 Oct 2010
Posts: 15302
Own Kudos [?]: 68054 [0]
Given Kudos: 442
Location: Pune, India
Re: A certain company assigns employees to offices in such a way [#permalink]
SoniaSaini
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
Responding to a pm:
Quote:
Let three employees be A,B,C

I will use separator to divide-
A,B,C,#

therefore answer- 4!/3! ( since order do not matter ) = 4

where am i going wrong by this logic

The two offices are distinct. When you use # to separate the employees of first and second office,
You have taken these cases: #ABC, A#BC, AB#C, ABC#

How About: B#AC, C#AB, BC#A, AC#B ?

You cannot use this method here.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3709
Own Kudos [?]: 17757 [0]
Given Kudos: 165
A certain company assigns employees to offices in such a way [#permalink]
• Approach using $$2^3$$already discussed. So giving another approach to this.

Given

• 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.

To Find

• The number of ways can the company assign 3 employees to 2 different offices.

Approach and Working Out

• There are 2 offices so an employee has 3 choices.
o Office 1, office 2, or nowhere.

• So 3 employees will have 3 × 3 = 9 choices.
o However, for a particular scenario, none of the employees will be assigned which is forbidden as the question suggests some of the offices can be empty.

• Answer = 9 – 1 = 8.

Intern
Joined: 23 Oct 2020
Posts: 21
Own Kudos [?]: 4 [0]
Given Kudos: 47
Re: A certain company assigns employees to offices in such a way [#permalink]
Bunuel
sagarsabnis
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 three employee can be assigned to either of the two offices, meaning that each employee has 2 choices --> 2*2*2=2^3=8.

Bunuel how would the answer to this question change if it said no more than one employee can be assigned to each office space ??
3*2= 6 ??
Math Expert
Joined: 02 Sep 2009
Posts: 95503
Own Kudos [?]: 658493 [1]
Given Kudos: 87257
Re: A certain company assigns employees to offices in such a way [#permalink]
1
Kudos
Michele4
Bunuel
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 three employee can be assigned to either of the two offices, meaning that each employee has 2 choices --> 2*2*2=2^3=8.