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Updated on: 24 May 2024, 11:22
Originally posted by EgmatQuantExpert on 18 Apr 2018, 05:24.
Last edited by Bunuel on 24 May 2024, 11:22, edited 7 times in total.
Last edited by Bunuel on 24 May 2024, 11:22, edited 7 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:47) correct
38%
(02:30)
wrong
based on 686
sessions
History
Date
Time
Result
Not Attempted Yet
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.
A. 45
B. 56
C. 64
D. 78
E. 96
A. 45
B. 56
C. 64
D. 78
E. 96
3 Deadly mistakes in Permutation and Combination - Exercise Question #2
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
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
Updated on: 23 Apr 2018, 04:42
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.
Last edited by EgmatQuantExpert on 23 Apr 2018, 04:42, edited 1 time in total.
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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
Hence, the correct answer is option C.
Answer: C
General Discussion
20 Apr 2018, 07:35
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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.
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.
