sagarsabnis 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 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
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.