Answer:
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\\", permutation(n, r));
printf("The Combination is = %d", combination(n, r));
}
Step-by-step 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=2
- The 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! = 6
- Next 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-r
- This 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 3
- It multiplies 3 by fact. fact is initialized to 1 So
- 1*3 = 3
- Then it decreases number=3 by 1 so number=2
- Now while loops checks if number>0 It is true as number is 2
- It multiplies 2 by fact. Value of fact is now 3 So
- 3*2 = 6
- Then it decreases number=2 by 1 so number=1
- Now while loops checks if number>0 It is true as number is 1
- It multiplies 1 by fact. Value of fact is now 6 So
- 6*1 = 6
- Then it decreases number=1 by 1 so number=0
- Now while loops checks if number>0 It is false as number is 0
- So 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.