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
Assign employees
-
- Master | Next Rank: 500 Posts
- Posts: 104
- Joined: Wed Feb 13, 2008 1:44 pm
- Thanked: 8 times
Either the 2question is incorrectly framed and should also consider the possibility that none of the employess are assigned to any office. That way the answer would be 5.
Else the answer should be 4 and i dont see that in the options!!
the 2 offices
Off 1, Off 2
No. of ways-
Off 1 - 3 , Off2 0
off1 - 2 , Off2 - 1
Off1 - 0, Off2 -3
Off1 - 1, Off2 - 2
Someone correct me if I m wrong!
Else the answer should be 4 and i dont see that in the options!!
the 2 offices
Off 1, Off 2
No. of ways-
Off 1 - 3 , Off2 0
off1 - 2 , Off2 - 1
Off1 - 0, Off2 -3
Off1 - 1, Off2 - 2
Someone correct me if I m wrong!
-
- Master | Next Rank: 500 Posts
- Posts: 104
- Joined: Wed Feb 13, 2008 1:44 pm
- Thanked: 8 times
Actually aatech is right. The answer is 8.
We are right in selecting cases but wrong in counting the number of arrangements in that case.
In second case
(2,1) and (1,2)
Each case inturn has 3 ways becos we are "arranging" people between 2 offices here.
So if E denotes Employee and O denotes office
Selecting E1 and E2 is not same as selecting E2 and E3.
So within the second case
1) 3 ways of arranging people in O1,O2
(a) O1 - E1 and O2-E2,E3
(b)O1-E2 and O2-E1,E3
(c)O1-E3 and O2-E1,E2
2) similar to above case but just reversed
(a) O1 - E2,E3, O2 - E1
(b) O1- E1,E3 O2-E2
(c)O1-E1,E2 O2- E3
We are right in selecting cases but wrong in counting the number of arrangements in that case.
In second case
(2,1) and (1,2)
Each case inturn has 3 ways becos we are "arranging" people between 2 offices here.
So if E denotes Employee and O denotes office
Selecting E1 and E2 is not same as selecting E2 and E3.
So within the second case
1) 3 ways of arranging people in O1,O2
(a) O1 - E1 and O2-E2,E3
(b)O1-E2 and O2-E1,E3
(c)O1-E3 and O2-E1,E2
2) similar to above case but just reversed
(a) O1 - E2,E3, O2 - E1
(b) O1- E1,E3 O2-E2
(c)O1-E1,E2 O2- E3
GMAT/MBA Expert
- lunarpower
- GMAT Instructor
- Posts: 3380
- Joined: Mon Mar 03, 2008 1:20 am
- Thanked: 2256 times
- Followed by:1535 members
- GMAT Score:800
that works, although it's certainly not self-explanatory enough as is.ektamatta wrote:there is another way to solve this problem
2 office
3 employees
2^3
8 ways
here's a fuller explanation:
let's call the offices 1 and 2.
for each employee, there's a choice of being assigned either to office 1 or to office 2. furthermore, wherever the previous employees are assigned has no effect upon the assignments of the other employees, since double-/triple-packing and empty offices are both fine.
therefore:
3 employees
2 options for each employee
multiply the #s of options, because they're independent sequential choices: 2 x 2 x 2 = 8 total sets of choices.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
-
- Master | Next Rank: 500 Posts
- Posts: 416
- Joined: Wed Oct 03, 2007 9:08 am
- Thanked: 10 times
- Followed by:1 members
I know this is an old post.
But with reference to Ron's reply
Each employee actually has 3 options.
To choose Office 1 or office 2 or none of the offices
So wouldn't that make the choice
3*3*3 .
Ron - Please let me why this is wrong?
But with reference to Ron's reply
Each employee actually has 3 options.
To choose Office 1 or office 2 or none of the offices
So wouldn't that make the choice
3*3*3 .
Ron - Please let me why this is wrong?
-
- Newbie | Next Rank: 10 Posts
- Posts: 7
- Joined: Sat Aug 14, 2010 3:34 am
Hi gmatrant,gmatrant wrote:I know this is an old post.
But with reference to Ron's reply
Each employee actually has 3 options.
To choose Office 1 or office 2 or none of the offices
So wouldn't that make the choice
3*3*3 .
Ron - Please let me why this is wrong?
came across this thread.There is a 99% possibility that u must have already aced the gmat and I know the qs is almost a year old ,but still replying to this one.
each employee has to belong to an office and so he can choose either office 1 or office 2.
Not choosing office 1 will imply that he belongs to office 2 and vice versa.
Hope this makes things clear..
Cheers!
LUNARPOWER UR FACE IS LIKE SNOOPDOG..LOKKS LIKE A ROCKSTAR
lunarpower wrote:that works, although it's certainly not self-explanatory enough as is.ektamatta wrote:there is another way to solve this problem
2 office
3 employees
2^3
8 ways
here's a fuller explanation:
let's call the offices 1 and 2.
for each employee, there's a choice of being assigned either to office 1 or to office 2. furthermore, wherever the previous employees are assigned has no effect upon the assignments of the other employees, since double-/triple-packing and empty offices are both fine.
therefore:
3 employees
2 options for each employee
multiply the #s of options, because they're independent sequential choices: 2 x 2 x 2 = 8 total sets of choices.
A REPLY BY tictaktoe
REALLY EASY TO UNDERSTAND IN THIS WAY.
let x,y b office and A,B AND C be employyes
OFFICE X ------ OFFICE Y
ABC ----- nil
nil------- ABC
AB------- C
CA --------B
BC --------A
A ---------BC
C ---------AB
B ---------CA
REALLY EASY TO UNDERSTAND IN THIS WAY.
let x,y b office and A,B AND C be employyes
OFFICE X ------ OFFICE Y
ABC ----- nil
nil------- ABC
AB------- C
CA --------B
BC --------A
A ---------BC
C ---------AB
B ---------CA
- talaangoshtari
- Master | Next Rank: 500 Posts
- Posts: 154
- Joined: Wed May 21, 2014 4:29 am
- Thanked: 8 times
- Followed by:1 members
Why is 3^2 wrong? If we assume that we have 2 slots, for 2 offices. For each office we can assign 3 people, 3 × 3 = 9