Abhijit K 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
Since the greatest answer choice is 9, there can be at most 9 ways to distribute the 3 employees.
Implication:
We can WRITE OUT all of the possible distributions.
Let the 3 employees be A, B and C.
Distributions with A in the first office:
ABC - none
AB - C
AC - B
A - BC
Total ways = 4.
Distributions with A in the second office:
none - ABC
C - AB
B - AC
BC - A
Total ways = 4.
Since A must be in either the first office or the second office, all of the possible distributions have been counted.
Total ways = 4+4 = 8.
The correct answer is
D.
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