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A dormitory has n students, all of whom like to gossip. One of the students hears a rumor, and tells it to one of the other n -1 students picked at random. Subsequently, each student who hears the rumor tells it to a student picked at random from the dormitory (excluding, of course, himself/ herself and the person from whom he/ she heard the rumor). Let pr be the probability that the rumor is told r times without coming back to a student who has already heard it from a dormitory mate. So p1 = p2 = 1, and pn = 0.
a) Find a formula for pr for r between 3 and n - 1.
b) Estimate this probability for n = 300 and r = 30.
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