2023 CUBRMC Team #4 four share meals
Source:
March 8, 2024
combinatoricscubrmc
Problem Statement
Alice, Bob, Carol, and David decide that they will share meals and that one of them will cook each night. Because David enjoys cooking, he will cook on days of the week, while Alice, Bob, and Carol each pick a day of the week to cook on. If Alice, Bob, and Carol each choose the day they cook uniformly at random so as to avoid overlap, what is the probability that David does not cook on three consecutive days? For example, Monday, Tuesday and Wednesday are considered as three consecutive days, so are Saturday, Sunday and Monday.