152 views
number of distinct binary tree,that can be created by 5 nodes(distinct)

$5$ 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 $= \binom {2n}{n}*n!$
0
Could you please elaborate this solution numerically?
+2

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.

0
Bell no. gives partitions. It doesnt consider permutations.

+1 vote