Factorials. The following set of problems relates to computing factorials. If you did not...

Factorials. The following set of problems relates to computing factorials. If you did not cover the section on recursion, read the material on pages 200–201 for the definition of a factorial and then review the nonrecursive function for computing the factorial.

Whereas permutations (Problem) are concerned with order, combinations are not. Thus, given n distinct objects, there is only one combination of n objects taken n at a time, but there are n! permutations of n distinct objects taken n at a time. The number of combinations of n objects, taken k at a time is equal to n!/((k!)(n ‒ k)!). Write a function named combine that receives values for n and k and then returns the number of combinations of the n objects taken k at a time. (If we consider the set of digits {1,2,3}, the different combinations of two digits are {1,2},{1,3} and {2,3} Assume that the corresponding prototype is

int combine(int n, int k);

Problem

Factorials. The following set of problems relates to computing factorials. If you did not cover the section on recursion, read the material on pages 200–201 for the definition of a factorial and then review the nonrecursive function for computing the factorial.

Suppose that we have n distinct objects. There are many different orders that we can select to line up the objects in a row. In fact, there are n! orderings, or permutations, that can be obtained with n objects. If we have n objects, and select k of the objects, then there are n!/(n ‒ k)! possible orderings of k objects. That is, the number of different permutations of n different objects taken k at a time is n!/(n ‒ k)!.Write a function named permute that receives values for n and k, and then returns the number of permutations of the n objects taken k at a time. (If we consider the set of digits {1,2,3}, the different permutations of two digits are {1,2},{2,1},{1,3},{3,1},{2,3} and {3,2} Assume that the corresponding prototype is

int permute(int n,int k);