In one of my posts on C Programming, I showed, how to calculate the Factorial of a number.

In this post we will use that program, and extend it to calculate the Combination and the Permutation .

If you haven’t read the post on factorial calculation, then you can check it out here.

Now, a combination is defined as:

and the Permutation is defined as:

So we will have the user enter their choice, and then prompt the user to enter the and

and then return the answer based on their choice.

The program is pretty simple and can be written as shown below.

### PROGRAM:

/************************************ ****PERMUTATION AND COMBINATION***** ***********************************/ #include<stdio.h> /*Function that calculates the factorial of a given integer n */ double factorial(int n){ int i; double fact=1; for(i=n;i>=1;i--){ fact=fact*i; } return fact; } int main(){ int n,r,choice; printf("\n\nType 1 for Permutation and \n2 for Combination\n"); scanf("%d",&choice); if(choice==1){ printf("Enter n and r for nPr\n"); scanf("%d %d",&n,&r); if(r>n){ printf("Sorry! r should be smaller than n\n"); return 0; } printf("The permutation (%dP%d)= %f\n",n,r,factorial(n)/factorial(r)); }else if(choice==2){ printf("Enter n and r for nCr\n"); scanf("%d %d",&n,&r); if(r>n){ printf("r should be smaller than n\n"); return 0; } printf("The combination (%dC%d)= %f\n",n,r,factorial(n)/(factorial(n-r)*factorial(r))); } else{ printf("\nPlease enter a valid choice!\n"); } }

As one can see, the program is pretty much self-explanatory.

### OUTPUT:

Some sample outputs have been attached below: