1. In a binary tree with exactly 15 internal nodes, 10 of them have 2 children, and the other 5 have 1 child. How many leaf nodes are there in the tree?
2. Generalize your answer for part (a). In a binary tree with x + y internal nodes, where x of them have 2 children, and y of them have 1 child, how many leaf nodes are there?
3. Prove your answer to part (b). It is recommended you use induction on n.