  Let $T$ be a random tree taken uniformly at random from the family of
labelled trees on $n$ vertices. In this note, we provide bounds for $c(n)$, the
number of sub-trees of $T$ that hold asymptotically almost surely. With
computer support we show that $1.41805386^n \le c(n) \le 1.41959881^n$.
Moreover, there is a strong indication that, in fact, $c(n) \le 1.41806183^n$.
