Spread of rumors. In a town of n + 1 inhabitants, a person tells a rumor to a second person, who in turn repeats it to a third person, etc. At each step the recipient of the rumor is chosen at random from then people available. Find the probability that the rumor will be told r times with out:

(a) returning to the originator,

(b) being repeated to any person. Do the same problem when at each step the rumor is told by one person to a gathering of N randomly chosen people. (The first question is the special case N = 1.)