Problem Solving

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

D

its 2*2*2 =8
each has two choices

each employee has 8 choices i guess...

frank1 wrote:each employee has 8 choices i guess...

there are three employees say A,B,and C and 2 offices say X , and Y
now A can chose any from x and y in 2c1=2 ways
similarly B in 2 ways and C in 2 ways
so total # of ways=2*2*2=8

it will come down to basics
i mean
1 ----------- 2
ABC ----------- 0
0 ----------- ABC
AB ----------- C
C ----------- AB
BC ----------- A
A ----------- BC
CA ----------- B
B ----------- CA

take A,
he infact can make 8 choices.

Am i missing some basics here? (may be wrong choice of word)

frank1 wrote:it will come down to basics
i mean
1 ----------- 2
ABC ----------- 0
0 ----------- ABC
AB ----------- C
C ----------- AB
BC ----------- A
A ----------- BC
CA ----------- B
B ----------- CA

take A,
he infact can make 8 choices.

Am i missing some basics here? (may be wrong choice of word)

Every employee has to go to one of the office. so if A choses not to go to office x then that means he has chosen to go to office y.

So consider following choices for A:
1. go to x (means do not go to y) = do not got y (means go to x).
2. go to y(means do not go to x) = do not go to x (means go to y).
3. do not got to x and Y (THIS CONDITION IS NOT POSSIBLE)