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According to Cayley's Formula :-

Total Number of possible trees with 'n' labeled nodes = $n^{n-2}$   , $n\geq2$

It can be proved by Prufer Sequences.

@ankitgupta.1729

brother, in the question they didn't mention that it is binary tree ===> you took an arbitrary tree

right?

Sir, In question, it is asked about a tree, not a binary tree. binary tree is rooted and ordered.

It is a well-known Cayley's formula to find total number of possible trees if vertices are labeled. In case of rooted trees , this formula becomes $n^{n-2} * n = n^{n-1}$ because any of the n vertices can be selected as a root.

I am attaching the screenshot from the Graph Theory book by Narsingh Deo.

PFA.

https://en.wikipedia.org/wiki/Cayley's_formula

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