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at a circular dinner table, five couples are seated randomly

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doomedcat
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at a circular dinner table, five couples are seated randomly [#permalink] New post   22 May 2018, 22:52
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38% (01:49) correct 62% (01:44) wrong based on 114 sessions
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at a circular dinner table, five couples are seated randomly. What is the probability that everybody sits next to his or her partner?

A\(\frac{24}{10!}\)

B\(\frac{24}{9!}\)

C\(\frac{48}{9!}\)

D\(\frac{48}{10!}\)

E\(\frac{768}{9!}\)

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GyMrAT
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Re: at a circular dinner table, five couples are seated randomly [#permalink] New post   22 May 2018, 23:35
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Answer: E

10 persons can be arranged at a circular table in (10-1)!= 9! ways, hence

Total Outcomes = (10-1)! = 9!

Favorable condition is when the partners sit next to each of their respective partners,

Lets first arrange the 5 wives at the circular table, which can be done in (5-1)!=4!

Now the husbands can be seated next to their wives in two ways, on the left or on the right of their wives. Hence 2 ways for each wife & since there are 5 wives, therefore \(2^5\) ways

Favorable outcomes = \(4! * 2^5\) = 768

Therefore the required probability = \(768/9!\)
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Re: at a circular dinner table, five couples are seated randomly [#permalink] New post   23 May 2018, 00:09
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doomedcat wrote:
at a circular dinner table, five couples are seated randomly. What is the probability that everybody sits next to his or her partner?

A\(\frac{24}{10!}\)

B\(\frac{24}{9!}\)

C\(\frac{48}{9!}\)

D\(\frac{48}{10!}\)

E\(\frac{768}{9!}\)

Source : Experts Global


Check other Arrangements in a Row and around a Table questions in our Special Questions Directory.
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BjornMattsson
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at a circular dinner table, five couples are seated randomly [#permalink] New post   21 Jul 2019, 12:54
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Hey I used the following approach 1. Pick any person and sit them down. The probability is then 1/9 that the person to be seated next to nr1 is his wife. 2. Pick any other person. The probability is then 1/7 that the person picked to sit next to nr2 is her husband. If we keep going like this we end up with the probabilities (1/9 * 1/7 * 1/5 * 1/3 * 1/1).

Multiply by 2 because of the scenario of having the partner on the other side of you, this yields the answer 2/945 = 7/9!


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Re: at a circular dinner table, five couples are seated randomly [#permalink] New post   17 Sep 2023, 00:35
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Re: at a circular dinner table, five couples are seated randomly [#permalink]
17 Sep 2023, 00:35
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