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

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
At a circular dinner table, three couples are seated randomly  [#permalink]

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12 Apr 2018, 12:08
5
00:00

Difficulty:

55% (hard)

Question Stats:

42% (01:37) correct 58% (02:16) wrong based on 46 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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12 Apr 2018, 23:21
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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24 Apr 2018, 20:25
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, 20:25
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# At a circular dinner table, three couples are seated randomly

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