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furious_tiles
bedtime for midgets:
Each of the seven midgets sleeps in his own bed in a shared dormitory. Every night, they retire to bed one at a time, always in the same sequential order, with the youngest midget retiring first and the oldest retiring last. On a particular evening, the youngest midget is in a jolly mood. He decides not to go to his own bed but rather to choose one at random from among the other six beds. As each of the other midgets retires, he chooses his own bed if it is not occupied, and otherwise chooses another unoccupied bed at random.
What is the probability that the oldest midget sleeps in his own bed?
What is the expected number of midgets who do not sleep in their own beds?