Question: Seated at random at a round table with n seats are n people, among them John and Mary. (i) Answer questions (i)(iv) of Problem 3.2.5.

Seated at random at a round table with n seats are n people, among them John and Mary. (i) Answer questions (i)–(iv) of Problem 3.2.5. Anything peculiar about the answer to (iii)? (ii) Assume that n = 2k. Find the probability that John and Mary sit facing each other (e.g., numbers 1 and 7 on the clock). (iii) Assume that n = 8. Find the probability that good friends, Nico, Noah, and Helen, are not separated by other guests.

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