permutations and combination

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naaga: Master | Next Rank: 500 Posts; Posts: 129; Joined: Mon Dec 15, 2008 11:43 pm; Location: Hyderabad; Thanked: 2 times

permutations and combination

by naaga » Tue Mar 03, 2009 6:06 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

friends please explain , I am getting only 4 ways but the OA is A

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Source: Beat The GMAT — Problem Solving | Tue Mar 03, 2009 6:06 am

kamu: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Fri Feb 27, 2009 12:41 am; Thanked: 44 times; Followed by:3 members

by kamu » Tue Mar 03, 2009 6:11 am

Hi,
there are two offices and three employees.
so three employees can be assigned to one room(say A) in 1 way
in the same way three employees can be assigned to one room(say B) in 1 way
and
two employees can be put in one room(A) and one employee in another room(B) in 3C1*2C2 ways=3
and
two employees can be put in one room(B) and one employee in another room(A) in 3C1*2C2 ways=3
total is 1+1+3+3=8 ways.