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M61-19

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M61-19  [#permalink]

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New post 18 Jun 2018, 05:08
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

50% (01:21) correct 50% (01:38) wrong based on 8 sessions

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5 couples sit on 10 chairs around a round table. If each couple must be seated together, how many possible arrangements are there?


A. 256
B. 512
C. 768
D. 1,024
E. 1,080

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Math Revolution GMAT Instructor
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Re M61-19  [#permalink]

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New post 18 Jun 2018, 05:08
Official Solution:


5 couples sit on 10 chairs around a round table. If each couple must be seated together, how many possible arrangements are there?


A. 256
B. 512
C. 768
D. 1,024
E. 1,080


The number of arrangements of the 5 couples in a circle is \((5-1)! = 4!\). The members of each couple can be arranged in \(2!\) ways. Thus, the total number of arrangements is \(4! * 2! * 2! * 2! * 2! * 2! = 24*2*2*2*2*2 = 768\).


Answer: C
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Re: M61-19  [#permalink]

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New post 20 Oct 2019, 14:49
Is there a simpler way to solve this problem? It is not clear for me
Thank you
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Re M61-19  [#permalink]

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New post 24 Oct 2019, 05:54
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. can someone please explain the solution?
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Re: M61-19  [#permalink]

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New post 04 Nov 2019, 11:51
Since couples have to sit together you can think question as it asks for how many arrangements with 5 people is possible in a table at first. Since this is a round table (not a line) 5 people can sit chairs with 4! different arrangements. If it would be a line, number of arrangements would be 5! however, in a round table, every 4 of 5 different arrangements would be the same unlike a line (this is not very easy to understand). Shortly, 4! makes 24 and in the second step, since every element of our arrangements (I mean couples) has two members, they actually can change their places while sitting together. So, for every couple you should add (2) as multiplier to the number of arrangements which in total makes 4!x2^5.
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Re: M61-19   [#permalink] 04 Nov 2019, 11:51
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