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Three elves who work at Santa's factory are having a festive feast, and each one invites their best friend who works at the University of the North Pole. The three elves and their besties sit down at a round table. All of the possible seating arrangements of the six party-goers are equally likely.
(a) Show that the probability that each elf sits next to their bestie is $\frac 2 {15}$.
(b) Find the probability that exactly two of Santa's elves sit next to their best friends.
(c) Find the probability that no elf sits next to their best friend.
Based on STEP Mathematics I, 2008, Q13. Question reproduced by kind permission of Cambridge Assessment Group Archives. The question remains Copyright University of Cambridge Local Examinations Syndicate ("UCLES"), All rights reserved.