AAPL wrote: ↑Sat Dec 12, 2020 2:34 pm
GMAT Prep
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
D
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)
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
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https://www.beatthegmat.com/counting-pro ... 44302.html
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https://www.beatthegmat.com/picking-a-5- ... 73110.html
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https://www.beatthegmat.com/permutation- ... 57412.html
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https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
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https://www.beatthegmat.com/combinatoric ... 73194.html
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https://www.beatthegmat.com/arabian-hors ... 50703.html
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https://www.beatthegmat.com/sub-sets-pro ... 73337.html
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https://www.beatthegmat.com/combinatoric ... 73180.html
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https://www.beatthegmat.com/digits-numbers-t270127.html
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https://www.beatthegmat.com/doubt-on-sep ... 71047.html
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https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
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https://www.beatthegmat.com/wonderful-p- ... 71001.html
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https://www.beatthegmat.com/permutation- ... 73915.html
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https://www.beatthegmat.com/permutation-t122873.html
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https://www.beatthegmat.com/no-two-ladie ... 75661.html
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https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
