A certain company assigns employees to offices in such a way

BTGmoderatorDC 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 D

Source: Official Guide

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

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MEDIUM
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DIFFICULT
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Cheers,
Brent

BTGmoderatorDC 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

ASIDE: When the answer choices are small, you should also consider listing and counting

Let X, Y and Z be the 3 employees.
Let A and B be the 2 offices.

We'll list the possible outcomes as follows: (employees in office A | employees in office B)
So, we get:
( XYZ | -- )
( XY |Z )
( XZ | Y )
( YZ | X )
( Z | XY )
( Y | XZ )
( X | YZ )
( -- | XYZ )

Answer: D

Cheers,
Brent