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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 ^{N}C_4  .
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

 




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