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Number of quadrilateral formed with N distinct points on circumference of Circle
• Last Updated : 15 Mar, 2021

Given an integer N which denotes the points on the circumference of a circle, the task is to find the number of quadrilaterals formed using these points.
Examples:

Input: N = 5
Output: 5
Input: N = 10
Output: 210

Approach: The idea is to use permutation and combination to find the number of possible quadrilaterals using the N points on the circumference of the circle. The number of possible quadrilaterals will be .
Below is the implementation of the above approach:

## C++

 `// C++ implementation to find the``// number of quadrilaterals formed``// with N distinct points``#include``using` `namespace` `std;` `// Function to find the factorial``// of the given number N``int` `fact(``int` `n)``{``    ``int` `res = 1;` `    ``// Loop to find the factorial``    ``// of the given number``    ``for``(``int` `i = 2; i < n + 1; i++)``       ``res = res * i;``       ` `    ``return` `res;``}` `// Function to find the number of``// combinations in the N``int` `nCr(``int` `n, ``int` `r)``{``    ``return` `(fact(n) / (fact(r) *``                       ``fact(n - r)));``}` `// Driver Code``int` `main()``{``    ``int` `n = 5;` `    ``// Function Call``    ``cout << (nCr(n, 4));``}` `// This code is contributed by rock_cool`

## Java

 `// Java implementation to find the``// number of quadrilaterals formed``// with N distinct points``class` `GFG{``    ` `// Function to find the number of``// combinations in the N``static` `int` `nCr(``int` `n, ``int` `r)``{``    ``return` `(fact(n) / (fact(r) *``                       ``fact(n - r)));``}` `// Function to find the factorial``// of the given number N``static` `int` `fact(``int` `n)``{``    ``int` `res = ``1``;` `    ``// Loop to find the factorial``    ``// of the given number``    ``for``(``int` `i = ``2``; i < n + ``1``; i++)``        ``res = res * i;``    ``return` `res;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``5``;` `    ``// Function Call``    ``System.out.println(nCr(n, ``4``));``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 implementation to find the``# number of quadrilaterals formed``# with N distinct points` `# Function to find the number of``# combinations in the N``def` `nCr(n, r):``    ``return` `(fact(n) ``/` `(fact(r)``                ``*` `fact(n ``-` `r)))` `# Function to find the factorial``# of the given number N``def` `fact(n):``    ``res ``=` `1``    ` `    ``# Loop to find the factorial``    ``# of the given number``    ``for` `i ``in` `range``(``2``, n ``+` `1``):``        ``res ``=` `res ``*` `i    ``    ``return` `res` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``n ``=` `5``    ` `    ``# Function Call``    ``print``(``int``(nCr(n, ``4``)))`

## C#

 `// C# implementation to find the``// number of quadrilaterals formed``// with N distinct points``using` `System;``class` `GFG{``    ` `// Function to find the number of``// combinations in the N``static` `int` `nCr(``int` `n, ``int` `r)``{``    ``return` `(fact(n) / (fact(r) *``                       ``fact(n - r)));``}` `// Function to find the factorial``// of the given number N``static` `int` `fact(``int` `n)``{``    ``int` `res = 1;` `    ``// Loop to find the factorial``    ``// of the given number``    ``for``(``int` `i = 2; i < n + 1; i++)``        ``res = res * i;``    ``return` `res;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 5;` `    ``// Function Call``    ``Console.Write(nCr(n, 4));``}``}` `// This code is contributed by shivanisinghss2110`

## Javascript

 ``
Output:
`5`

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