What Is the Probability of Two Specific People Sitting Next to Each Other?

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In a group of six people sitting around a table, the probability of two specific individuals sitting next to each other is calculated as 2/5. This is derived from the total arrangements of 5! and considering the two individuals as a single unit, leading to 4! arrangements and the possibility of swapping them. Some participants suggested the answer is 1/5, but this is incorrect. The correct reasoning involves recognizing that one of the specific individuals has two neighbors, making the probability of the other being adjacent 2 out of 5. Thus, the accurate probability is confirmed as 2/5.
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Homework Statement


A group comprising 6 peoiple is sitting around a table. Find the probability that two particular people are sitting next to each other.


Homework Equations





The Attempt at a Solution



4!2!/5!=2/5 because total number of possibities is 5!. If 2 people are to be next to each other than there are 5 groups so 4! choices with each choice, one can swap the group of two. So times by 2!.


BUt the answers suggested 1/5
 
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Some really dubious 'answers' are being suggested to you. The answer is clearly 2/5. Pick one of the particular people. There are 2 people sitting next to him and 3 not. The odds the other particular person is in the former group is 2/5.
 
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That is a nice way of doing it.
 

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