The number of possible ordered trees with 3 nodes A,B,C

Question

amount of time it would take to send 500 packets using 6-packet size window and without sliding window will be, when the time to send in one direction is 5 ms

31000, 5000

4600, 21600

5000, 30000

30000, 5000.......... pls explain the logic behind?

Answer 1

No. of BST = 2nCn/n+1 = 6C3/4 = 5 
 

No. of Binary tree = (2nCn/(n+1))n! = (6C3/4)*3!= 30

Comments

BUT answer for this is 12 ..What does ordered trees means here??

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an ordered tree is one in which node(root) is connected by disjoint set of subtree. 

In ordered tree (a "tree" of the first definition) has the subtrees in a particular order, and the subtree sequence cannot contain the same tree twice, because the subtrees must be disjoint. A rooted tree does not have these restrictions; by this definition a root might have a subtree twice, in a structure that resembles a cycle.

I am getting 10 as answer.

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It will 12.

Case-1: Given the root node has two children,(A(root)->B(left)->C(right) and A(root)->B(right)->C(left))So there are 3*2 = 6 possible ordered trees

Case-2: GIven the root node has one child(A(root)->B(left)->C(left) and A(root)->B(left)->C(leftt)), so there are a total of 3*2 = 6 possible ordered trees with three nodes given that the root node has only one child.

In case-2,A(root)->B(left)->C(left)  and (root)->B(right)->C(right) are considered as same as subsequence are not disjoint.