  An $r$-matching in a graph $G$ is a collection of edges in $G$ such that the
distance between any two edges is at least $r$. A $2$-matching is also called
an induced matching. In this paper, we estimate the maximum number of
$r$-matchings in a tree of fixed order. We also prove that the $n$-vertex path
has the maximum number of induced matchings among all $n$-vertex trees.
