  Suppose we are given the free product V of a finite family of finite or
countable sets. We consider a transient random walk on the free product arising
naturally from a convex combination of random walks on the free factors. We
prove the existence of the asymptotic entropy and present three different,
equivalent formulas, which are derived by three different techniques. In
particular, we will show that the entropy is the rate of escape with respect to
the Greenian metric. Moreover, we link asymptotic entropy with the rate of
escape and volume growth resulting in two inequalities.
