Number of quadrilateral formed with N distinct points on circumference of Circle

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 = 5Output:5Input:N = 10Output: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<bits/stdc++.h>` `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

`<script>` `// JavaScript implementation to find the` `// number of quadrilaterals formed` `// with N distinct points` `// Function to find the factorial` `// of the given number N` `function` `fact(n)` `{` ` ` `let res = 1;` ` ` `// Loop to find the factorial` ` ` `// of the given number` ` ` `for` `(let i = 2; i < n + 1; i++)` ` ` `res = res * i;` ` ` ` ` `return` `res;` `}` `// Function to find the number of` `// combinations in the N` `function` `nCr(n, r)` `{` ` ` `return` `(fact(n) / (fact(r) *` ` ` `fact(n - r)));` `}` `// Driver Code` ` ` `let n = 5;` ` ` `// Function Call` ` ` `document.write(nCr(n, 4));` `// This code is contributed by Surbhi Tyagi.` `</script>` |

**Output:**

5