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# M30-02

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Math Expert
Joined: 02 Sep 2009
Posts: 44321

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16 Sep 2014, 01:45
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Difficulty:

75% (hard)

Question Stats:

49% (01:19) correct 51% (01:48) wrong based on 37 sessions

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Nine family members: 5 grandchildren (3 brothers and 2 sisters) and their 4 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?

A. 120
B. 480
C. 1440
D. 2880
E. 8640
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44321

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16 Sep 2014, 01:45
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Official Solution:

Nine family members: 5 grandchildren (3 brothers and 2 sisters) and their 4 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?

A. 120
B. 480
C. 1440
D. 2880
E. 8640

Consider two brothers and two sisters between them as one unit: {BSSB}.

So, now we have 6 units: {G}, {G}, {G}, {G}, {B}, and {BSSB}.

These 6 units can be arranged around a circular table in $$(6-1)!=5!$$ ways.

Next, analyze {BSSB} unit:

We can choose 2 brothers out of 3 for the unit in $$C^2_3=3$$ ways;

These brothers, within the unit, can be arranged in 2! ways: $$\{B_1, S, S, B_2\}$$ or $$\{B_2, S, S, B_1\}$$.

The sisters, within the unit, also can be arranged in 2! ways: $$\{B, S_1, S_2, B\}$$ or $$\{B, S_2, S_1, B\}$$.

Therefore, the final answer is 5!*3*2*2=1440.

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Senior Manager
Joined: 31 Mar 2016
Posts: 405
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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07 Jul 2016, 10:26
I think this is a high-quality question and I agree with explanation. Hi Bunuel, can you please post some detailed theory on such circular permutations? Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 44321

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07 Jul 2016, 10:35
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Senthil7 wrote:
I think this is a high-quality question and I agree with explanation. Hi Bunuel, can you please post some detailed theory on such circular permutations? Thanks

Check other Arrangements in a Row and around a Table questions in our Special Questions Directory.

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Hope it helps.
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Intern
Joined: 06 May 2016
Posts: 14

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03 Aug 2016, 13:17
I think this is also possible {b,g,s,g,s,g,g,b},b
"2 sisters are seated between any two of the three brothers"

am I missing anything?
Intern
Joined: 24 Oct 2016
Posts: 12

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27 Nov 2016, 01:33
No word in the question specifies whether two sisters can be seated jointly or not. The question needs to be rephrased so that it would be clearer.
Intern
Joined: 04 Apr 2017
Posts: 18

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19 Oct 2017, 05:01
I think this is a poor-quality question and I agree with explanation. The question does not specify whether there can be anyone between the two sisters.
Re M30-02   [#permalink] 19 Oct 2017, 05:01
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# M30-02

Moderators: chetan2u, Bunuel

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