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# A teacher assigns students to rooms in such a way that some

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Director
Joined: 17 Oct 2005
Posts: 928
A teacher assigns students to rooms in such a way that some [#permalink]

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20 Jan 2006, 04:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A teacher assigns students to rooms in such a way that some of the rooms can be empty and more than one student can be assigned to a room. In how many ways can the teacher assign 3 students to 2 different rooms?
Director
Joined: 17 Dec 2005
Posts: 547
Location: Germany

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20 Jan 2006, 06:20
Is it 8?

2Â³=8, each student can be assigned to two rooms, without restrictions.
Senior Manager
Joined: 03 Nov 2005
Posts: 384
Location: Chicago, IL

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20 Jan 2006, 15:58
Edit: First, i thought there 3 different romms instead of 2.
C (3:2)=3 (ways to choose 2 students out of 3)
AB/C, AC/B, BC/A
However, the order of rooms matter and there 2 ways to assign 2 students together and 1 student in 2 separate rooms
R#1 R#2
AB/ C
C/ AB

Total no. of ways=3*2=6
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Hard work is the main determinant of success

CEO
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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20 Jan 2006, 17:49
Two possible cases

1. All 3 in a single room - 2 cases
2. 2 in one room and 1 in one room. - 3C2 * 2 = 6 cases

Total = 8
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

SVP
Joined: 16 Oct 2003
Posts: 1801

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20 Jan 2006, 20:23
Is it 8?

2Â³=8, each student can be assigned to two rooms, without restrictions.

I also got 8.

Hey allabout. How did you get this 2Â³ I mean 2 raise to 3.
Intern
Joined: 29 Sep 2005
Posts: 10
Location: Paris

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21 Jan 2006, 11:15
Can somebody tell me which possibility i am missing, if the answer is eight.

3,0
0,3
1,2
2,1
VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA

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21 Jan 2006, 11:34
Bhai wrote:
Is it 8?

2Â³=8, each student can be assigned to two rooms, without restrictions.

I also got 8.

Hey allabout. How did you get this 2Â³ I mean 2 raise to 3.

Bhai,

I think the explanation goes like this:
For each student there are 2 choices: Room 1 or Room 2

Hence Total choices = 2 * 2 * 2 = 8.
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA

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21 Jan 2006, 11:39
prash_c wrote:
Can somebody tell me which possibility i am missing, if the answer is eight.

3,0
0,3
1,2
2,1

Here is I think all the possibilities are:

Students: A, B, C
Rooms: 1, 2

ABC, None
None, ABC
A, BC
B, AC
C, AB
AB, C
AC, B
BC, A
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Director
Joined: 04 Oct 2005
Posts: 582
Location: Chicago

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22 Jan 2006, 00:00
its 2^3=8 choices..
SVP
Joined: 16 Oct 2003
Posts: 1801

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22 Jan 2006, 00:18
giddi77 wrote:
Bhai wrote:
Is it 8?

2Â³=8, each student can be assigned to two rooms, without restrictions.

I also got 8.

Hey allabout. How did you get this 2Â³ I mean 2 raise to 3.

Bhai,

I think the explanation goes like this:
For each student there are 2 choices: Room 1 or Room 2

Hence Total choices = 2 * 2 * 2 = 8.

I meant hos did he get 3 over 2. we write 2^3. See how allabout did 3 little above 2. I think you can do it only if you copy from somewhere it was already formatted.
VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA

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22 Jan 2006, 00:32
Bhai wrote:
giddi77 wrote:
Bhai wrote:
Is it 8?

2Â³=8, each student can be assigned to two rooms, without restrictions.

I also got 8.

Hey allabout. How did you get this 2Â³ I mean 2 raise to 3.

Bhai,

I think the explanation goes like this:
For each student there are 2 choices: Room 1 or Room 2

Hence Total choices = 2 * 2 * 2 = 8.

I meant hos did he get 3 over 2. we write 2^3. See how allabout did 3 little above 2. I think you can do it only if you copy from somewhere it was already formatted.

Hmm. That part I don't know I am not good at formatting stuff anyways...
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

22 Jan 2006, 00:32
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