  A leaf of a plane tree is called an old leaf if it is the leftmost child of
its parent, and it is called a young leaf otherwise. In this paper we enumerate
plane trees with a given number of old leaves and young leaves. The formula is
obtained combinatorially by presenting two bijections between plane trees and
2-Motzkin paths which map young leaves to red horizontal steps, and old leaves
to up steps plus one. We derive some implications to the enumeration of
restricted permutations with respect to certain statistics such as pairs of
consecutive deficiencies, double descents, and ascending runs. Finally, our
main bijection is applied to obtain refinements of two identities of Coker,
involving refined Narayana numbers and the Catalan numbers.
