Assigning 3 employees to 2 offices

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Fri May 15, 2009 10:19 pm

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

Answer seems to be D. Can anyone explain the logci pls? Tx

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Source: Beat The GMAT — Problem Solving | Fri May 15, 2009 10:19 pm

francopiccolo: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Dec 11, 2008 12:02 am; Thanked: 1 times

by francopiccolo » Fri May 15, 2009 11:16 pm

You can assign employees in two different ways:

(i) 3 employees to one office and 0 to the other office.
(ii) 2 employees to one office and 1 to the other office.

For (i), You can put the employees on the 1st or 2nd office, those are two ways of arranging the employees.

For (ii) you have to consider the possible combinations of 2 from 3 = 3!/2!(3-2)! = 3. And you can assign those possible combinations to office 1 or 2, therefore you have 6 possible ways of assigning the employees.

So we have a total of 8 ways of assigning employees.

(D)

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aj5105: Legendary Member; Posts: 1169; Joined: Sun Jul 06, 2008 2:34 amFollowed by: 1 member; Thanked: 25 times

by aj5105 » Fri May 15, 2009 11:19 pm

This is how it goes:

1 way: Emp1 Emp2 Emp3
2 way: Emp3 Emp1 Emp2

3 way: Emp1 Emp3 Emp2
4 way: Emp2 Emp1 Emp3

5 way: Emp3 Emp2 Emp1
6 way: Emp1 Emp3 Emp2

7 way: Emp1 Emp2 Emp3. No body on the other office.
8 way: No boby in the first and all 3 in the second.

bold: Office 1

unbold: Office 2

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Mon May 18, 2009 10:53 am

thanks guys!

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