Consider the following problem: How many ways can a committee of four people be selected f...

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:

where the exclamation point denotes the factorial function. Moreover, C(n, 0) = C(n, n) = 1. It is also known that C(n, r) = 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).