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## Perm & Comb

##### This topic has expert replies
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### Perm & Comb

by csandeepreddy » Sat Sep 20, 2008 8:10 am
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

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### Re: Perm & Comb

by amitdgr » Sat Sep 20, 2008 8:33 am
csandeepreddy wrote: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
3 people to fill 2 places

must be 3P2 = 6 not sure though. Whats the OA ?
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by stop@800 » Sat Sep 20, 2008 8:58 am
There are 4 possible arrangements:

Off1 off2
0 3
1 2
2 1
3 0

1st can be done in 1 way
2nd can be done in 3 way
3rd can be done in 3 way
4th can be done in 1 way

Total 8 ways

Whats the OA?

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by csandeepreddy » Sat Sep 20, 2008 9:18 am
Hello "stop@800".

You are right, the answer is 8.

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by sogmat » Wed Dec 03, 2008 7:10 pm
We clould also do the above as follows

2 offices
3 employess

case1- 0 in first office and 3 in the other- this can be done in 2 ways
case2- 2 in first office and 1 in the other- this can be done in 3C2*2C1=6

So total ways= 2+6=8

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by logitech » Wed Dec 03, 2008 8:17 pm
You can also think like:

Every office has three chairs. So we can 3,2,1, or NOBODY sitting on them = 4 options for each office. We have 2 office; so the answer is 8.
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by canuckclint » Fri Dec 12, 2008 9:20 pm
logitech wrote:You can also think like:

Every office has three chairs. So we can 3,2,1, or NOBODY sitting on them = 4 options for each office. We have 2 office; so the answer is 8.
But you can't have nobody and nobody so this isn't correct.

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by earth@work » Sat Dec 13, 2008 11:08 am
let ABC be 3 people
total arrangements: (AB-C), (AC-B), (BC-A) =3*2=6
(ABC-0) = 1*2=2
TOTAL 6+2=8

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