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# At a circular dinner table, three couples are seated randomly

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BSchool Forum Moderator
Joined: 26 Feb 2016
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At a circular dinner table, three couples are seated randomly [#permalink]

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12 Apr 2018, 13:08
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Difficulty:

45% (medium)

Question Stats:

22% (00:37) correct 78% (01:41) wrong based on 18 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
[Reveal] Spoiler: OA

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

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13 Apr 2018, 00:21
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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.
Re: At a circular dinner table, three couples are seated randomly   [#permalink] 13 Apr 2018, 00:21
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# At a circular dinner table, three couples are seated randomly

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