3. (rumor spreading) in a town with n + 1 inhabitants, a person decides to spread a rumor. the first person picks one of the other n inhabitants uniformly at random and tells him the rumor. the second person in turn picks one of the other (n-1) inhabitants (other than himself and his source) uniformly at random and tells them the rumor. this process of spreading the rumor continues k times in total. assume k a n (a) what is the probability that the rumor did not reach the original source of the rumor? (b) what is the probability that the rumor was never repeated to a person? (i. e. all picks were those that haven't heard the rumor before)