The combination of n objects, such as balls in a basket, taken k at a time can be calculated recursively using the formula shown in Figure 2-16. This is a useful formula. For example, several state...

The combination of n objects, such as balls in a basket, taken k at a time can be calculated recursively using the formula shown in Figure 2-16. This is a useful formula. For example, several state lotteries require players to choose six numbers out of a series of possible numbers. This formula can be used to calculate the number of possible combinations, k, of n objects. For example, for 49 numbers, there are C(49, 6), or 13,983,816, different combinations of six numbers. Write a recursive algorithm to calculate the combination of n objects taken k at a time.