you can solve this question by, initially considering nodes as unlabeled , then by catalan rule no. of trees =2nCn/(n+1) , and remember if no. of nodes is m then in catalan no. we put n=m-1.

Put n=3 , we will get 5 trees

now , as we know these nodes are labeled so we start arranging (permuting) them on these 5 trees.

The question is not clear. Is it asking for binary trees?

WELL its a question of ISRO2014 .. i just copied nd paste... so question is same as in ISRO question paper...

120.that rule is for binary tree i guess..

@shivanijaiswal1234 I am not getting your answer.

Why Catalan rule? Can you draw 5 tree skeletons ?

Can you explain it with more details ?

@shweta1920 @shivanijaiswal1234

I think that if nothing is given we can go with the structural definition of tree.

So number of trees will be n

^{n-2}.Read this,

http://www-math.mit.edu/~djk/18.310/18.310F04/counting_trees.html

yes, i assumed it to be binary tree, as if it would be n-ary tree then

4! *4^{2 }then no option is matchingIn case of binay tree, answer will be 336.

ye question ... ny smjh ara .. ;(