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There are Fifteen seats at a round table. There are three people already seated, their locations chosen uniformly at random.

Three people wish to join the table and sit next to each other. What is the probability that they can do so without anyone else having to move?

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  • $\begingroup$ If there are 15 seats, its not possible for three people to cover all possible gaps of 3. If you try to have only 2 spaces between the three already-seated people, you will inevitably leave at least three adjacent seats available somewhere at the table. Are the three additional people also sitting at random, yet they want to sit next to each other? $\endgroup$ – user76844 Oct 28 '13 at 13:48
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Community wiki answer so the question can be marked as answered:

As user76844 pointed out in a comment, the probability is $1$ since the $3$ people already seated cannot block all opportunities for $3$ people to sit next to each other.

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