**C Program to calculate Binomial coefficient**

**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 : :**

- 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
of the function.**recursive call**

- 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*

*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 : :**

**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 : :**

**SOURCE CODE : :**

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/* 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 : :**

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************* 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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