By | 25.03.2017

# C Program to calculate Binomial coefficient

Write a C Program to calculate Binomial coefficient using Recursion. Here’s simple Program to calculate Binomial coefficients using Recursion in C Programming Language.

## Recursion : :

• Recursion is the process of repeating items in a self-similar way. In programming languages, if a program allows you to call a function inside the same function, then it is called a recursive call of the function.
• The C programming language supports recursion, i.e., a function to call itself. But while using recursion, programmers need to be careful to define an exit condition from the function, otherwise it will go into an infinite loop.
• Recursive functions are very useful to solve many mathematical problems, such as calculating the factorial of a number, generating Fibonacci series, etc.

## Binomial Coefficient

Following are common definition of Binomial Coefficients : :

1) A binomial coefficients C(n, k) can be defined as the coefficient of X^k in the expansion of (1 + X)^n.

2) A binomial coefficients C(n, k) also gives the number of ways, disregarding order, that k objects can be chosen from among n objects; more formally, the number of k-element subsets (or k-combinations) of an n-element set.

### Problem : :

Write a function that takes two parameters n and k and returns the value of Binomial Coefficient C(n, k). For example, your function should return 6 for n = 4 and k = 2, and it should return 10 for n = 5 and k = 2.

Below is the source code for C Program to calculate Binomial coefficient using Recursion which is successfully compiled and run on Windows System to produce desired output as shown below :

### SOURCE CODE : :

```/* C Program to calculate Binomial coefficient using Recursion */

#include<stdio.h>
int BC(int n, int k);

int main()
{
int n,k;
printf("Enter n and k : ");
scanf("%d%d",&n,&k);
printf("%\nBinomial coefficient\n",BC(n,k));
printf("%d\n",BC(n,k));

return 0;
}

int BC(int n, int k)
{
if(k==0 || k==n)
return 1;
return BC(n-1,k-1) + BC(n-1,k);
}```

### OUTPUT  : :

```************* OUTPUT **************

************* FIRST RUN ***********

Enter n and k :
4
2

Binomial coefficient
6

************* SECOND RUN ***********

Enter n and k :
8
4

Binomial coefficient
70```

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