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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2812
A certain company assigns projects to employees such that more than on  [#permalink]

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Updated on: 13 Aug 2018, 06:28
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:52) correct 41% (02:20) wrong based on 98 sessions

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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
Joined: 04 Jan 2015
Posts: 2812
Re: A certain company assigns projects to employees such that more than on  [#permalink]

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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.

_________________

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
Joined: 01 Feb 2018
Posts: 75
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 4
WE: Consulting (Consulting)
Re: A certain company assigns projects to employees such that more than on  [#permalink]

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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
Joined: 04 Jan 2015
Posts: 2812
Re: A certain company assigns projects to employees such that more than on  [#permalink]

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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
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Joined: 30 Jul 2017
Posts: 20
Re: A certain company assigns projects to employees such that more than on  [#permalink]

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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
Joined: 04 Jan 2015
Posts: 2812
Re: A certain company assigns projects to employees such that more than on  [#permalink]

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

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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.

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
Joined: 17 Jan 2016
Posts: 2
A certain company assigns projects to employees such that more than on  [#permalink]

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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?

A certain company assigns projects to employees such that more than on   [#permalink] 14 Apr 2019, 03:39
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