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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, 06:30
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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
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Re: Arrangements around the table [#permalink] New post 04 Oct 2010, 09:01
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, 09:06
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, 09:47
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...
Re: Arrangements around the table   [#permalink] 04 Oct 2010, 09:47
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