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A teacher assigns students to rooms in such a way that some [#permalink]
20 Jan 2006, 03:39

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?

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

"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."

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."

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.

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."