Write two functions called permutation() and combination(), where permutation() computes and returns n!/(n-r)!whereas combination() returns. n!/(n-r)!r!A third function called par_input() gets the input values for n and r. An example of correct program behavior follows: Input: 3 2 Output: The permutation is 6, and the combination is 3.

Here is the program in C.

#include<stdio.h>   // header file used to input output operations

int permutation(int n, int r);  // function to computer permutation

int combination(int n, int r);  //function to compute combination

int factorial(int number);  // function to computer factorial

void par_input(int n, int r);    // function take take input value of n and r

int main()  //start of main() function body

{    

   int n,r;  // declare n and r variables

   par_input(n,r);  //calls par_input() function to get values of n and r

}

 

int permutation(int n, int r)   // method to calculate permutation

{

   return factorial(n) / factorial(n-r);  //formula for permutation

}

 

int combination(int n, int r)  // method to calculate combination

{

   return permutation(n, r) / factorial(r); //formula for combination

}

 

int factorial(int number)  // to find factorial of a number

{

   int fact = 1;      

   while(number > 0)  //loop continues until value of number gets <=0

   {

       fact = fact *number;  

       number--;

   }      

   return fact;

}

void par_input(int n, int r)  //function to take input values

{

   printf("Enter n: ");  //prompts user to enter the value of n

   scanf("%d", &n);      //reads the value of n from user

   printf("Enter r: "); ////prompts user to enter the value of r

   scanf("%d", &r); //reads the value of r from user

  //calls the combination and permutation methods to display results

   printf("The permutation is = %d\n", permutation(n, r));    

   printf("The Combination is = %d", combination(n, r));      

}

Explanation:

The main() function calls par_input() function. This function asks user to enter values of n and r and then calls permutation() and combination() methods to compute the combination and permutation using these input values. Lets say user enters n=3 and r=2The permutation() function computes and returns permutation using the following formula: n! / (n-r)! factorial(n) / factorial(n-r); This function calls factorial method which calculates the factorial of n and n-r.This function then returns the permutation.3! / (3-2)! = 3*2*1 / 1! = 6Next the combination() function computes and returns combination using the following formula: n! / r! * (n - r)!permutation(n, r) / factorial(r)This function calls permutation() and factorial() methods which calculate the combination of n and n-rThis function then returns the combination.3! / 2! * (3-2)! = 3*2*1 / 2*1 * 1 = 6 / 2 = 3 Factorial function computes and returns the factorial of n, r and n-r.Lets take n! When n=3 So this function computes factorial as follows:while loops checks if number>0 It is true as number is 3It multiplies 3 by fact. fact is initialized to 1 So1*3 = 3Then it decreases number=3 by 1 so number=2Now while loops checks if number>0 It is true as number is 2It multiplies 2 by fact. Value of fact is now 3 So3*2 = 6Then it decreases number=2 by 1 so number=1Now while loops checks if number>0 It is true as number is 1It multiplies 1 by fact. Value of fact is now 6 So6*1 = 6Then it decreases number=1 by 1 so number=0Now while loops checks if number>0 It is false as number is 0So the loop breaks and the value of fact is returned.As fact= 6 So factorial of n is 6.

The output of the program is attached in the screen shot.

It would be 10 inches

11: a which it you