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number of distinct binary tree,that can be created by 5 nodes(distinct)
asked in Graph Theory by Veteran (20.4k points) 12 77 174 | 127 views

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$5$ distinct nodes means you can uniquely identify each node based on some parameter say a key value, Then the solution to this problem is given by bell's number.

Number of binary trees possible $= \binom {2n}{n}*n!$
answered by Boss (9.1k points) 4 63 205
Could you please elaborate this solution numerically?

I think its not correct.

#unlabelled binary trees possible = nth catalan number

Now, being labelled , they cn be permuted in n! ways.

So, answer = $\frac{\binom{2n}{n}}{n+1} * n!$

Correct me if wrong.

Bell no. gives partitions. It doesnt consider permutations.

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