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At a circular dinner table, three couples are seated randomly

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Senior PS Moderator
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V
Joined: 26 Feb 2016
Posts: 3188
Location: India
GPA: 3.12
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At a circular dinner table, three couples are seated randomly  [#permalink]

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New post 12 Apr 2018, 13:08
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

41% (01:27) correct 59% (02:25) wrong based on 40 sessions

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At a circular dinner table, three couples are seated randomly. What is the probability that each person sat adjacent to his/her partner?

A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{15}\)
D. \(\frac{2}{15}\)
E. \(\frac{1}{30}\)

Source: Experts Global

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Re: At a circular dinner table, three couples are seated randomly  [#permalink]

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New post 13 Apr 2018, 00:21
3
Total Number of outcomes will be :-
5! (since in circular permutation we use (n-1)! and here n=6)

Favorable outcomes:
2!(circular permutation of 3 groups)* 2!^3(ordering within each group)

Answer:-
(2!^4)/(5!) =16/120=2/15.

Therefore, Option D will be the correct answer.

Hope it helps.
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Re: At a circular dinner table, three couples are seated randomly  [#permalink]

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New post 24 Apr 2018, 21:25
Circluar table
So fix one pair other have two options to sit so 2 cases
Also each pair can sit two ways MF OR FM so 2 cases for each pair
So total valid cases: 2*2*2*2=16

Total cases- 5! as total 6 ppl are there and circle takes (n-1)!

So probability=16/120
=2/15

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Re: At a circular dinner table, three couples are seated randomly &nbs [#permalink] 24 Apr 2018, 21:25
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