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Seven family members are seated around their circular dinner

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Seven family members are seated around their circular dinner [#permalink] New post 04 Oct 2010, 05:30
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Question Stats:

56% (01:39) correct 44% (01:04) wrong based on 145 sessions
Seven family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?

A. 120
B. 240
C. 360
D. 480
E. 720
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 07:43, edited 1 time in total.
Edited the OA.
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Re: Arrangements around the table [#permalink] New post 04 Oct 2010, 08:01
eladshush wrote:
Seven family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?

A. 120
B. 240
C. 360
D. 480
E. 720


Are you sure you got the right OA on this one ?

As I see it : 7 members, and Michael & Bobby sit together. So treat those two like a single person. Now you have to arrange 6 people around a table. This may be done in 5! or 120 ways

The number of ways to arrange Michael & Bobby is 2 (MB or BM).

So net there are 240 ways or B

I don't think this is a GMAT level question, may be a tad too hard
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Re: Arrangements around the table [#permalink] New post 04 Oct 2010, 08:06
Expert's post
eladshush wrote:
Seven family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?

A. 120
B. 240
C. 360
D. 480
E. 720


Glue Michael and Bobby so that they create one unit, so we would have total of 6 units: {1}{2}{3}{4}{5}{MB} --> # of different arrangements of n objects around the table (circular arrangements) is is (n-1)!, so our 6 objects can be arranged in (6-1)!=5!.

On the other hand Michael and Bobby in 2! ways --> total 5!*2!=240.

Answer: B.

Similar question also posted by you: ways-to-sit-around-the-table-102187.html
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Re: Arrangements around the table [#permalink] New post 04 Oct 2010, 08:47
D is the OA for this question (I double checked), but I suspected it's wrong.

I also got 240 ways to arrange them around the table...
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Re: Seven family members are seated around their circular dinner [#permalink] New post 21 Sep 2013, 12:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Seven family members are seated around their circular dinner   [#permalink] 21 Sep 2013, 12:27
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