In the previous question, we saw that in the worst case, if we inserted the numbers in sorted (or reverse sorted) order, the height of the BST would be O(n). In the best case, the height would be (log(n)). What about the average case? We can compute the average case height by looking at all possible permutations of n numbers, calculating the height of each BST, and then averaging those heights. To keep things simple, we'll look at a specific number of nodes: when n = 3. (a) (10 points) Draw all possible BSTs that can be created by inserting 1,2,3 in different orders. (b) (3 points) What is the average height? (Sum of all heights / number of BSTs)