I'm trying to resolve an example from book.
T = (V, E) is a full binary tree, and
|V| = n. Show that there exist
n!/2^((n-1)/2) full orderings on V which extend transverse ordering.
As I know there are three main types of full orderings - post-, -pre, symmetrical. Having binary tree with root A and two leaves B, C. As I understand only order of leaves can change.
So for preorder we get
A < B < C; A < C < B.
C < B < A; B < C < A;
B < A < C; C < A < B.
Finally we get 6 different full orderings, but according to the formula should get
(1 * 2 * 3) / 2 ^ ((3-1)/2) = 3. Can anyone help me, maybe I misunderstand conditions of the task?