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M30-02

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M30-02 [#permalink]

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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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Re M30-02 [#permalink]

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New post 16 Sep 2014, 00:45
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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.


Answer: C
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Collection of Questions:
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Re M30-02 [#permalink]

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New post 07 Jul 2016, 09:26
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

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Re: M30-02 [#permalink]

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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.

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: M30-02 [#permalink]

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New post 03 Aug 2016, 12:17
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?

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Re: M30-02 [#permalink]

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New post 27 Nov 2016, 00:33
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.

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Re M30-02 [#permalink]

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New post 19 Oct 2017, 04:01
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.

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Re M30-02   [#permalink] 19 Oct 2017, 04:01
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