19.2 Draw all binary search trees that can result from inserting permutations of 1, 2, 3, and 4. How many trees are there? What are the probabilities of each trees occurring if all permutations are equally likely?

(10 points) Exercise 19.2 included finding the probability (based on equally likely insertion orders of each of the 24 permutations) of each of the 14 different trees that can result when inserting the numbers 1, 2, 3, and 4 into an initially empty BST (with no re-balancing).

(a) With the same assumption (that all permutations of the four numbers are equally likely), what is the (weighted) average height of the BSTs?

(b) With the same assumptions, do the same exercise for inserting the four numbers into an AVL tree. In other words, what is the average height of the AVL trees?