Question: Tyrion, Cersei, and ten other people are sitting at a round table, with their seating arrangement having been randomly assigned. What is the probability that Tyrion and Cersei are sitting next to each other? Find this in two ways:
(a) using a sample space of size 12!, where an outcome is fully detailed about the seating;
(b) using a much smaller sample space, which focuses on Tyrion and Cersei.