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There are 5 couples. If they sit on 10 chairs around a round table suc

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Math Revolution GMAT Instructor
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There are 5 couples. If they sit on 10 chairs around a round table suc  [#permalink]

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New post 05 Feb 2018, 02:12
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (01:47) correct 50% (02:04) wrong based on 35 sessions

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[GMAT math practice question]

There are 5 couples. If they sit on 10 chairs around a round table such that each couple sits side by side, how many possible cases are there?

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

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Re: There are 5 couples. If they sit on 10 chairs around a round table suc  [#permalink]

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New post 05 Feb 2018, 03:30
2
2
We can find in how many ways 5 objects may be placed around a circular table: (5-1)! = 4! = 24.
Then two people in each couple may sit in two ways (AB and BA), so we should multiply 24 by 2^5
24*32 = 768

Answer C
Math Revolution GMAT Instructor
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Re: There are 5 couples. If they sit on 10 chairs around a round table suc  [#permalink]

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New post 07 Feb 2018, 00:47
=>

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.

Therefore, the answer is C.

Answer: C
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Re: There are 5 couples. If they sit on 10 chairs around a round table suc &nbs [#permalink] 07 Feb 2018, 00:47
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