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Dinner Party Seating

A host invites \(n\) guests to a party (guest #1, guest #2, … , guest #n). Each guest brings with them their best friend. At the party there is a large circular table with \2n\) seats. All of the \(n\) invited guests and their best friends sit in a random seat.

  1. What is the probability that guest #1 is seated next to their best friend?
  2. What is the expected number of the \(n\) invited guests who are seated next to their best friend?

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