I don't see how

Cayley's formula is applicable because it talks about all possible trees on n vertices, not

*rooted* trees derived from a given tree.

The adjective "non-isomorphic" cannot be applied to just one tree. It is NOT the case that a tree is non-isomorphic if no other trees are isomorphic to it. Rather, the question is asking to find a set of trees that a

*pairwise* non-isomorphic. For example, trees with root 1 and 3 are non-isomorphic because they have a different path length from the root to the vertex with three leaves.