Following are common definition of Binomial Coefficients.

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

Given two numbers n and r, find value of ^{n}C_{r}

**Examples :**

Input : n = 5, r = 2 Output : 30 The value of 5C2 is 10 Input : n = 3, r = 1 Output : 3

The idea is simply based on below formula.

^{n}C_{r}= (n!) / (r! * (n-r)!)

## C++

`// CPP program To calculate The Value Of nCr ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `fact(` `int` `n); ` ` ` `int` `nCr(` `int` `n, ` `int` `r) ` `{ ` ` ` `return` `fact(n) / (fact(r) * fact(n - r)); ` `} ` ` ` `// Returns factorial of n ` `int` `fact(` `int` `n) ` `{ ` ` ` `int` `res = 1; ` ` ` `for` `(` `int` `i = 2; i <= n; i++) ` ` ` `res = res * i; ` ` ` `return` `res; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 5, r = 3; ` ` ` `cout << nCr(n, r); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program To calculate ` `// The Value Of nCr ` `class` `GFG { ` ` ` `static` `int` `nCr(` `int` `n, ` `int` `r) ` `{ ` ` ` `return` `fact(n) / (fact(r) * ` ` ` `fact(n - r)); ` `} ` ` ` `// Returns factorial of n ` `static` `int` `fact(` `int` `n) ` `{ ` ` ` `int` `res = ` `1` `; ` ` ` `for` `(` `int` `i = ` `2` `; i <= n; i++) ` ` ` `res = res * i; ` ` ` `return` `res; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `n = ` `5` `, r = ` `3` `; ` ` ` `System.out.println(nCr(n, r)); ` `} ` `} ` ` ` `// This code is Contributed by ` `// Smitha Dinesh Semwal. ` |

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## Python 3

`# Python 3 program To calculate ` `# The Value Of nCr ` ` ` `def` `nCr(n, r): ` ` ` ` ` `return` `(fact(n) ` `/` `(fact(r) ` ` ` `*` `fact(n ` `-` `r))) ` ` ` `# Returns factorial of n ` `def` `fact(n): ` ` ` ` ` `res ` `=` `1` ` ` ` ` `for` `i ` `in` `range` `(` `2` `, n` `+` `1` `): ` ` ` `res ` `=` `res ` `*` `i ` ` ` ` ` `return` `res ` ` ` `# Driver code ` `n ` `=` `5` `r ` `=` `3` `print` `(` `int` `(nCr(n, r))) ` ` ` `# This code is contributed ` `# by Smitha ` |

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## C#

`// C# program To calculate ` `// The Value Of nCr ` `using` `System; ` ` ` `class` `GFG { ` ` ` `static` `int` `nCr(` `int` `n, ` `int` `r) ` `{ ` ` ` `return` `fact(n) / (fact(r) * ` ` ` `fact(n - r)); ` `} ` ` ` `// Returns factorial of n ` `static` `int` `fact(` `int` `n) ` `{ ` ` ` `int` `res = 1; ` ` ` `for` `(` `int` `i = 2; i <= n; i++) ` ` ` `res = res * i; ` ` ` `return` `res; ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `n = 5, r = 3; ` ` ` `Console.Write(nCr(n, r)); ` ` ` `} ` `} ` ` ` `// This code is Contributed by nitin mittal. ` |

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## PHP

`<?php ` `// PHP program To calculate ` `// the Value Of nCr ` ` ` ` ` `function` `nCr( ` `$n` `, ` `$r` `) ` `{ ` ` ` `return` `fact(` `$n` `) / (fact(` `$r` `) * ` ` ` `fact(` `$n` `- ` `$r` `)); ` `} ` ` ` `// Returns factorial of n ` `function` `fact( ` `$n` `) ` `{ ` ` ` `$res` `= 1; ` ` ` `for` `( ` `$i` `= 2; ` `$i` `<= ` `$n` `; ` `$i` `++) ` ` ` `$res` `= ` `$res` `* ` `$i` `; ` ` ` `return` `$res` `; ` `} ` ` ` ` ` `// Driver code ` ` ` `$n` `= 5; ` ` ` `$r` `= 3; ` ` ` `echo` `nCr(` `$n` `, ` `$r` `); ` ` ` `// This code is contributed by vt_m. ` `?> ` |

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**Output:**

10

**More Efficient Solutions:**

Dynamic Programming | Set 9 (Binomial Coefficient)

Space and time efficient Binomial Coefficient

All Articles on Binomial Coefficient

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