Number of triangles in a plane if no more than two points are collinear

Given n points in a plane and no more than two points are collinear, the task is to count the number of triangles in a given plane.

Examples:

Input :  n = 3
Output : 1

Input :  n = 4
Output : 4

Number of Triangles



Let there are n points in a plane and no three or more points are collinear then number of triangles in the given plane is given by  ^{n}\textrm{C}_{3} = \frac{n(n-1)(n-6)}{6}

C++

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// C++ program to find the number of
// triangles in a plane if no more
// then two points are collinear.
#include <bits/stdc++.h>
using namespace std;
  
// Function to find number of triangles
// in a plane.
int countNumberOfTriangles(int n)
{
  
    // Formula to find number of triangles
    // nC3 = n * (n - 1) * (n - 2) / 6
    return n * (n - 1) * (n - 2) / 6;
}
  
// Driver code
int main()
{
    int n = 4;
    cout << countNumberOfTriangles(n);
    return 0;
}

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Java

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// Java program to find the number of
// triangles in a plane if no more
// then two points are collinear.
import java.io.*;
  
class GFG {
  
    // Function to find number of triangles
    // in a plane.
    static int countNumberOfTriangles(int n)
    {
  
        // Formula to find number of triangle
        // nC3 = n * (n - 1) * (n - 2) / 6
        return n * (n - 1) * (n - 2) / 6;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int n = 4;
  
        System.out.println(
            countNumberOfTriangles(n));
    }
}

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Python3

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# Python3 program to find 
# the number of triangles 
# in a plane if no more
# then two points are collinear.
  
# Function to find number
# of triangles in a plane.
def countNumberOfTriangles(n) :
      
    # Formula to find 
    # number of triangles
    # nC3 = n * (n - 1) *
    # (n - 2) / 6
    return (n * (n - 1) * 
                (n - 2) // 6)
  
# Driver Code
if __name__ == '__main__' :
      
    n = 4
    print(countNumberOfTriangles(n))
  
                  
# This code is contributed
# by ajit

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C#

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// C# program to find the 
// number of triangles in 
// a plane if no more then 
// two points are collinear.
using System;
  
class GFG 
{
  
    // Function to find number
    // of triangles in a plane.
    static int countNumberOfTriangles(int n)
    {
  
        // Formula to find number 
        // of triangle 
        // nC3 = n * (n - 1) *
        //           (n - 2) / 6
        return n * (n - 1) * 
                   (n - 2) / 6;
    }
  
    // Driver code
    public static void Main()
    {
        int n = 4;
  
        Console.WriteLine(
            countNumberOfTriangles(n));
    }
}
  
// This code is contributed by anuj_67.

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PHP

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<?php
// PHP program to find the 
// number of triangles in a 
// plane if no more then 
// two points are collinear.
  
// Function to find number 
// of triangles in a plane.
function countNumberOfTriangles($n)
{
    // Formula to find number 
    // of triangles nC3 = n * 
    // (n - 1) * (n - 2) / 6
    return $n * ($n - 1) * 
                ($n - 2) / 6;
}
  
// Driver code
$n = 4;
echo countNumberOfTriangles($n);
  
// This code is contributed
// by anuj_67.
?>

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Output:

4


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