sagarsabnis
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 determine in how many ways the company can assign 3 employees to 2 different offices when some of the offices can be empty and more than one employee can be assigned to an office.
Since there are 3 people and 2 offices, we have 3 options for each office. Thus, the employees can be organized in 2^3 = 8 possible ways.
Alternative solution:
If you have trouble understanding why there should be 2^3 = 8 possible ways to assign 3 employees in 2 different offices, we can list all the possible ways one can assign 3 employees (say A, B and C) to 2 different offices (Office 1 and Office 2).
1) Office 1: A, B, C and Office 2: no one
2) Office 1: A, B and Office 2: C
3) Office 1: A, C and Office 2: B
4) Office 1: B, C and Office 2: A
5) Office 1: A and Office 2: B, C
6) Office 1: B and Office 2: A ,C
7) Office 1: C and Office 2: A, B
8) Office 1: no one and Office 2: A, B, and C
As we can see, there are 8 ways to assign 3 employees to 2 different offices.
Answer: D