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

It is currently 15 Oct 2019, 21:57

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

A certain company assigns projects to employees such that more than on

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post Updated on: 13 Aug 2018, 06:28
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:44) correct 39% (02:20) wrong based on 122 sessions

HideShow timer Statistics

3 Deadly mistakes in Permutation and Combination - Exercise Question #2


2- A certain company assigns projects to employees such that more than one or no employee can work on any project. In how many ways 3 employees will be assigned to 4 projects.

Options
    A. 45
    B. 56
    C. 64
    D. 78
    E. 96

Learn to use the Keyword Approach in Solving PnC question from the following article:


Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions

Article-3: 3 deadly mistakes you must avoid in Permutation & Combination

_________________

Originally posted by EgmatQuantExpert on 18 Apr 2018, 05:24.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:28, edited 6 times in total.
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
Re: A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post Updated on: 23 Apr 2018, 04:42

Solution



Given:
    • The company has to assign 3 employees to 4 projects
    • None or more than one employee can be assigned to any project.

To find:
    • The number of ways to assign 3 employees to 4 projects

Approach and Working:


Method-1)

Every employee can work in any of the 4 projects. Hence, 3 employees can work in 4*4*4=64 ways.

Method-2) By applying \(r^n\)

We have 3 employees or 3 objects that are to be arranged in 4 projects.

This is very similar to what we learnt in our article.

Thus,
    • n=3
    • r=4
And, total ways to arrange n objects into r things= \(4^3\)=64

Hence, the correct answer is option C.

Answer: C
_________________

Originally posted by EgmatQuantExpert on 18 Apr 2018, 05:30.
Last edited by EgmatQuantExpert on 23 Apr 2018, 04:42, edited 1 time in total.
Manager
Manager
User avatar
B
Joined: 01 Feb 2018
Posts: 73
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 4
WE: Consulting (Consulting)
Re: A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post 20 Apr 2018, 07:35
Pls post official solution :

this is how I worked :

Situation I : all 3 employees working:
# ways to choose 3 employees = 1
all three working of same project : 4 ways
all three working on different projects : 4 ways * 3 ways * 2 ways : 24 ways
2 working of same project & 1 working on different project : 4 ways * 3 ways : 12 ways

Total number of ways : 1*(4 + 24 + 12) = 40

Situation II : 2 out of 3 employees working:
# ways to choose 2 employees : 3 * 2 / 2 = 3
both working of same project : 4 ways
both working on different projects : 4 ways * 3 ways : 12 ways

Total number of ways : 3* (4 + 12) = 48

Situation III : 1 out of 3 employees working:
# ways to choose 1 employees : 3
working on any of the project : 4

Total number of ways : 3*(4) = 12

Situation IV : No employee working :
Total number of ways : 1


Sum of Situation I to IV : (40 + 48 + 12 + 1) = 101


I know its not in match with any of the possible solutions, pls help me to know where I have made mistake.
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
Re: A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post 20 Apr 2018, 22:38
GMAT215 wrote:
Pls post official solution :

this is how I worked :

Situation I : all 3 employees working:
# ways to choose 3 employees = 1
all three working of same project : 4 ways
all three working on different projects : 4 ways * 3 ways * 2 ways : 24 ways
2 working of same project & 1 working on different project : 4 ways * 3 ways : 12 ways

Total number of ways : 1*(4 + 24 + 12) = 40

Situation II : 2 out of 3 employees working:
# ways to choose 2 employees : 3 * 2 / 2 = 3
both working of same project : 4 ways
both working on different projects : 4 ways * 3 ways : 12 ways

Total number of ways : 3* (4 + 12) = 48

Situation III : 1 out of 3 employees working:
# ways to choose 1 employees : 3
working on any of the project : 4

Total number of ways : 3*(4) = 12

Situation IV : No employee working :
Total number of ways : 1


Sum of Situation I to IV : (40 + 48 + 12 + 1) = 101


I know its not in match with any of the possible solutions, pls help me to know where I have made mistake.


Hey GMAT215

I think you have misunderstood the question. I would request you to read it again and focus on the highlighted portion. :)

A certain company assigns projects to employees such that more than one or no employee can work on any project. In how many ways 3 employees will be assigned to 4 projects.

    The constraint in this question is that there could be a project in which more than one employee can work OR no one can work on that project!

    This however, does not mean that there could be a case where all 3 employees are working or 2 are working or 1 are working or 0 are working.

The constraint is on the project not on the people. We are explicitly saying that there 3 employees will be assigned to any of these 4 projects. We just need to find in how many ways, keeping in mind that there could be a project in which no one is working or more than one is working.

Keeping the above points in mind, can you try this question again?


Regards,
Saquib
Quant Expert
e-GMAT
_________________
Intern
Intern
avatar
B
Joined: 30 Jul 2017
Posts: 19
Re: A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post 21 Apr 2018, 06:26
reveal explanation to this question please.
According to me 1 employee has 4 options either go in any of the three or do not go at all so 4 ways
so for all three employees 4*4*4 =64 ways
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
Re: A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post 23 Apr 2018, 05:00
Intern
Intern
avatar
B
Joined: 12 Feb 2018
Posts: 1
Re: A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post 29 Apr 2018, 04:43
EgmatQuantExpert wrote:

Solution



Given:
    • The company has to assign 3 employees to 4 projects
    • None or more than one employee can be assigned to any project.

To find:
    • The number of ways to assign 3 employees to 4 projects

Approach and Working:


Method-1)

Every employee can work in any of the 4 projects. Hence, 3 employees can work in 4*4*4=64 ways.

Method-2) By applying \(r^n\)

We have 3 employees or 3 objects that are to be arranged in 4 projects.

This is very similar to what we learnt in our article.

Thus,
    • n=3
    • r=4
And, total ways to arrange n objects into r things= \(4^3\)=64

Hence, the correct answer is option C.

Answer: C


Hi, your solution does not seem to be correct, as it includes cases in which a project can have only 1 employee assigned to it.

I solved it as below:
To Each project (p1, p2, p3, p4), employees ( e1, e2, e3) can be assigned in following way:

For p1,
Case 1: all 3 emp assigned = 1 way
Case 2: 2 out of 3 emp assign = 3C2 = 3 ways
Case 3: no emp assigned = 1 way
Total ways for p1 = 5

Hence no. of ways employees can be assigned to 4 projects = 5^4 = 625
Intern
Intern
avatar
B
Status: As cheeks from my insta feed say: soon...
Joined: 17 Jan 2016
Posts: 46
A certain company assigns projects to employees such that more than on  [#permalink]

Show Tags

New post 14 Apr 2019, 03:39
Hello everyone,

My question is if the given were written as 4 projects spread over 3 employees, would the formula be 3^4?

Thanks in advance
GMAT Club Bot
A certain company assigns projects to employees such that more than on   [#permalink] 14 Apr 2019, 03:39
Display posts from previous: Sort by

A certain company assigns projects to employees such that more than on

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne