A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called.
(a) By how many different paths can a rumor travel through the group in three calls?
(b) By how many different paths can a rumor travel through the group in $N$ calls?
(c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?