TADM2E 5.3
From Algorithm Wiki
Induction proof:
Base case: Tree composed of just two nodes: x(root) and y. There is only one way x -> y
Assuming there is an unique path between x and y, we add a new leaf z under y. z is only connected to its parent y, so there is only one way from z to x that is z -> y->[unique path assumed]->x
