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(n-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:

Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

Permutation formula is wrong

Thanks a lot for the correction!

BTW thank you so much. Your programs mean a lot!!!

Permutation

n!/(n-r)!

Updated