Binary search trees

Question

the number of binary search trees with 4 nodes (1 , 2 , 3 , 4)  where 1 is always a leaf node?

Comments

Fix 1 as leaf node ( Its the lowest key so it will always be left child of some node in left subtree)

Permute the remaining 3 nodes using catalan number $\frac{\binom{2n}{n}}{n+1}$ using n=3

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bro i think there is a mistake " it will always be right child of some node in right subtree"

but i see what u intended, as we know 1 will be the leaf we just have to permute remaining nodes and form BST ryt?

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yeah sorry, now edited

Answer 1

Answer : 5

Only this combinations are possible.