Program to calculate value of nCr

• Difficulty Level : Easy
• Last Updated : 29 Jul, 2022

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

 `#include `   `int` `factorial(``int` `n) {` `      ``if``(n == 0)` `      ``return` `1;` `    ``int` `factorial = 1;` `    ``for` `(``int` `i = 2; i <= n; i++)` `        ``factorial = factorial * i;` `    ``return` `factorial;` `}`   `int` `nCr(``int` `n, ``int` `r) {` `    ``return` `factorial(n) / (factorial(r) * factorial(n - r));` `}`   `int` `main() {` `    ``int` `n = 5, r = 3;` `      ``printf``(``"%d"``, nCr(n, r));` `    ``return` `0;` `}`   `// This code was contributed by Omkar Prabhune`

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)` `{` `      ``if``(n==0)` `      ``return` `1;` `    ``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)` `{` `      ``if``(n==``0``)` `      ``return` `1``;` `    ``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):` `    ``if` `n ``=``=` `0``:` `        ``return` `1` `    ``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)` `{` `      ``if``(n==0)` `      ``return` `1;` `    ``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

 ``

Javascript

 ``

Output:

`10`

Time Complexity: O(n)

Auxiliary Space: O(1)

My Personal Notes arrow_drop_up
Recommended Articles
Page :