• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW
This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 85
Joined: 26 Mar 2008
Location: NJ, USA
Thanked: 1 times

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

User avatar
Master | Next Rank: 500 Posts
Posts: 228
Joined: 29 Jun 2008
Thanked: 15 times
Followed by:1 members

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 ?
Please visit my blog Gmat Tips and Strategies

User avatar
Legendary Member
Posts: 871
Joined: 13 Aug 2008
Thanked: 48 times

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?

Senior | Next Rank: 100 Posts
Posts: 85
Joined: 26 Mar 2008
Location: NJ, USA
Thanked: 1 times

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

You are right, the answer is 8.

Master | Next Rank: 500 Posts
Posts: 113
Joined: 21 Oct 2008
Location: Mumbai
Thanked: 1 times

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

User avatar
Legendary Member
Posts: 2134
Joined: 20 Oct 2008
Thanked: 237 times
Followed by:25 members
GMAT Score:730

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.
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

Master | Next Rank: 500 Posts
Posts: 154
Joined: 26 Aug 2008
Location: Canada
Thanked: 4 times

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.

User avatar
Master | Next Rank: 500 Posts
Posts: 248
Joined: 11 Aug 2008
Thanked: 13 times

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