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What is the total no. Of binary tree possible with n nodes? How one can calculate?
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It is nothing but counting number of unique structure possible

If we are talking about unlabled binary tree then there is formula for it $\frac{1}{n+1}^{2n}\mathbb{C}_{n}$

If we take n= 2 we get 2 unique structure

For n=3 fine unique structure

And. Labled binary search tree would be =$\frac{1}{n+1}^{2n}\mathbb{C}_{n}*n!$
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