this may be hit and try. any logical way of thinking, there is not that much of time there. what i thought is.
every vertex will have 2 choices to choose , as there will be (n-1) edges. every internal node have the choice to select any 2. as internal node will be having two edges so (n-1) (n-2) choices, while the 2 starting and end edge have (n-1) choice.
but can't get the formula.