Spreading the Rumor

In a town of $n$ inhabitants, a person tells a rumor to a second person, who in turn repeats it to a third person and so on. At each step the recipient of the rumor is chosen at random from the $n-1$ people available.

The probability that rumor will be told $n$ times without Returning to originator is $\left(a-\frac{n-b}{n-c}\right)^{n-c}$

Find the value of $a+b+c$