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There are $18$ padded chairs around a circular table, and the chairs are numbered from $1$ through $18$. How many ways can three people take their seats, so that no two people are adjacent?

 

You guys are my last resort. I have no clue how to solve this problem :(

 

Thank you so much!

 May 27, 2020
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 There are 18*17*16 ways to choose the three seats, if people can be adjacent.  We must subtract the cases where there are two people adjacent, which is 18*13*6.  So the number of ways is 18*17*16 - 18*13*6 = 3492.

 May 27, 2020

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