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A certain company assigns employees to offices in such a way that some
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04 Oct 2021, 04:41
04 Oct 2021, 04:41
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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
A. 5
B. 6
C. 7
D. 8
E. 9
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Re: A certain company assigns employees to offices in such a way that some
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04 Oct 2021, 05:38
04 Oct 2021, 05:38
Carcass 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
A. 5
B. 6
C. 7
D. 8
E. 9
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 GRE. So, be sure to learn it.
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Re: A certain company assigns employees to offices in such a way that some [#permalink]
04 Oct 2021, 05:38
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