Consider the following problem: How many ways can a committee of four people be selected from a group of 10 people? There are many other similar problems, where you are asked to find the number of ways to select a set of items from a given set of items. The general problem can be stated as follows: Find the number of ways r different things can be chosen from a set of n items, where r and n are nonnegative integers and r n. Suppose C(n, r) denotes the number of ways r different things can be chosen from a set of n items. Then C(n, r) is given by the following formula: Cðn; rÞ ¼ n! r!ðn rÞ! where the exclamation point denotes the factorial function. Moreover, C(n, 0) ¼ C(n, n) ¼ 1. It is also known that C(n, r) ¼ C(n – 1, r – 1) + C(n – 1, r). a. Write a recursive algorithm to determine C(n, r). Identify the base case(s) and the general case(s). b. Using your recursive algorithm, determine C(5, 3) and C(9, 4).