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A certain company assigns employees to offices in such a way

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Manager
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A certain company assigns employees to offices in such a way [#permalink] New post 17 May 2008, 01:51
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 fidderent offices?

a) 5
b) 6
c) 7
d) 8
e) 9
Intern
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Re: combinatorics/ employees [#permalink] New post 17 May 2008, 03:29
My answer would be D ie 8
The possible arrangements for the two offices could be..
3,0 - 1 way
1,2 - 3 ways
2,1 - 3 ways
0,3 - 1 way
So total 8 ways
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Re: combinatorics/ employees [#permalink] New post 17 May 2008, 09:57
OA is D

Could you please explain how you caoculate ways, for eample why for 1,2 - 3 ways and for 3,0 - 1 way?
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Re: combinatorics/ employees [#permalink] New post 17 May 2008, 17:48
For 1,2 - 3 ways let's say the people are m1,m2 and m3 so the arrangements could be
m1,m2 + m3
m2,m1 + m3
m3,m1 + m2
similar for 2,1

And for 3,0
only one arrangement is possible
m1+m2+m3,none
and similar for 0,3
hope it helps..let me know if doesn't
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Re: combinatorics/ employees [#permalink] New post 17 May 2008, 23:05
Why can't it be for 1,2?

m1,m2 +m3
m2,m1 + m3
m3,m1+m2
m3,m2+m1
m1,m3+m2
m2,m3+m1
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Re: combinatorics/ employees [#permalink] New post 18 May 2008, 19:44
It's not specified in the question that in a single office also..there are different arrangements possible....so
for eg..
m1,m2+m3 and
m1,m3+m2 are treated as same here.
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Re: combinatorics/ employees [#permalink] New post 18 May 2008, 21:46
alternatively ->

m1 can be assigned office in 2 ways
m2 can be assigned office in 2 ways
m3 can be assigned office in 2 ways

hence total ways of assigning them to offices = 2x2x2=8 ways
Re: combinatorics/ employees   [#permalink] 18 May 2008, 21:46
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