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
OA is D
Can an expert give a mathematical approach to, solve this question? Thanks in anticipation
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Hi Roland2rule,
When the answer choices to these types of questions are relatively small, you can use 'brute force' to list out all of the possibilities. Here, there are at least 4 options, but no more than 9, so if you're organized (and thorough with your work), then you should be able to list out all of the options without too much trouble.
We're asked to assign 3 employees to 2 rooms. (If we refer to the employees as A, B and C, the options would be...
0 in first room - A/B/C in the second room
1 in the first room:
A in first room - B/C in the second room
B in first room - A/C in the second room
C in first room - A/B in the second room
2 in the first room"
A/B in first room - C in the second room
A/C in first room - B in the second room
B/C in first room - A in the second room
A/B/C in first room - 0 in the second room
TOTAL OPTIONS = 1 + 3 + 3 + 1 = 8
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
When the answer choices to these types of questions are relatively small, you can use 'brute force' to list out all of the possibilities. Here, there are at least 4 options, but no more than 9, so if you're organized (and thorough with your work), then you should be able to list out all of the options without too much trouble.
We're asked to assign 3 employees to 2 rooms. (If we refer to the employees as A, B and C, the options would be...
0 in first room - A/B/C in the second room
1 in the first room:
A in first room - B/C in the second room
B in first room - A/C in the second room
C in first room - A/B in the second room
2 in the first room"
A/B in first room - C in the second room
A/C in first room - B in the second room
B/C in first room - A in the second room
A/B/C in first room - 0 in the second room
TOTAL OPTIONS = 1 + 3 + 3 + 1 = 8
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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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.BTGmoderatorRO 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
OA is D
Can an expert give a mathematical approach to, solve this question? Thanks in anticipation
Since there are 3 people and 2 offices, we have 2 options for each employee. Thus, the employees can be organized in 2 x 2 x 2 = 2^3 = 8 possible ways.
Answer: D
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Let X, Y and Z be the 3 employees.BTGmoderatorRO 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
OA is D
Can an expert give a mathematical approach to, solve this question? Thanks in anticipation
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)
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat- ... /video/775
You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776
Then you can try solving the following questions:
EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent