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 = 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 ^{N}C_4.



Below is the implementation of the above approach:

C++

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// 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

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Java

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// 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

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Python3

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# 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)))

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C#

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// 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

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Output:

5

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