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Program to calculate value of nCr
• Difficulty Level : Easy
• Last Updated : 22 Mar, 2021

Following are common definition of Binomial Coefficients

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

```Input :  n = 5, r = 2
Output : 10
The value of 5C2 is 10

Input : n = 3, r = 1
Output : 3```

The idea is simply based on below formula.

nCr = (n!) / (r! * (n-r)!)

## C++

 `// CPP program To calculate The Value Of nCr``#include ``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;``}`

## 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.`

## 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`

## 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.`

## PHP

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## Javascript

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Output:
`10`

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