TITLE: Probability that Ken and John set next to each other
QUESTION [19 upvotes]: A group of ten people sits down, uniformly at random, around a table. Ken
  and John are part of this group. Determine the probability that Ken and John sit
  next to each other.

There are $10!$ ways to arrange the seating for everyone, there are 10 possible ways for John and Ken to sit together.
$$\operatorname{Pr}(J\ \&\ K ) = \frac{10}{10!} = \frac{1}{9!}$$
Am I correct?

REPLY [57 votes]: Two of nine people sit next to John.  The probability that Ken is one of these two is $\frac29$.