alltimeacheiver 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
We need to count only the number of ways that the 3 employees can be assigned to the first office, since whoever isn't assigned to the first office must automatically be assigned to the second office.
Given
n elements, the number of ways to choose 0 or more of the
n elements = 2^
n.
Thus, given 3 people, the number of ways to choose 0 or more of them for the first office = 2^3 = 8.
We also could simply write out all the options for the first office. Given 3 people ABC, the following combinations could be assigned to the first office:
ABC
AB
AC
BC
A
B
C
None
Same answer: 8 ways.
The correct answer is
D.
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