I have to solve the following example:
"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 the n people available.
a) Find the probability that the rumor will be told r times without ever returning
to the originator."
The probability that the second person choose one, that is not the first one, must be (n-2)/(n+1) and also for the 3rd,4th,...,r person. So the final probability should be , correct?