Out of 8 given points if 5 points are collinear then the number of triangles that can be formed is

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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: 

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 

C++

#include <bits/stdc++.h>

using namespace std;

int countNumberOfTriangles(int n)

{

    return n * (n - 1) * (n - 2) / 6;

}

int main()

{

    int n = 4;

    cout << countNumberOfTriangles(n);

    return 0;

}

C

#include <stdio.h>

int countNumberOfTriangles(int n)

{

    return n * (n - 1) * (n - 2) / 6;

}

int main()

{

    int n = 4;

    printf("%d",countNumberOfTriangles(n));

    return 0;

}

Java

import java.io.*;

class GFG {

    static int countNumberOfTriangles(int n)

    {

        return n * (n - 1) * (n - 2) / 6;

    }

    public static void main(String[] args)

    {

        int n = 4;

        System.out.println(

            countNumberOfTriangles(n));

    }

}

Python3

def countNumberOfTriangles(n) :

    return (n * (n - 1) *

                (n - 2) // 6)

if __name__ == '__main__' :

    n = 4

    print(countNumberOfTriangles(n))

C#

using System;

class GFG

{

    static int countNumberOfTriangles(int n)

    {

        return n * (n - 1) *

                   (n - 2) / 6;

    }

    public static void Main()

    {

        int n = 4;

        Console.WriteLine(

            countNumberOfTriangles(n));

    }

}

PHP

<?php

function countNumberOfTriangles($n)

{

    return $n * ($n - 1) *

                ($n - 2) / 6;

}

$n = 4;

echo countNumberOfTriangles($n);

?>

Javascript

<script>

    function countNumberOfTriangles(n)

    {

        return n * (n - 1) * (n - 2) / 6;

    }

        var n = 4;

        document.write(countNumberOfTriangles(n));

</script>

Time complexity: O(1)

Auxiliary space: O(1)

1) 8C3

2) 8C3 – 5C3

3) 8C3 – 5C3 – 1

4) None of these

Answer: (3) 8C3 – 5C3 – 1

Solution: We have total of 8 points here. The number of points we need to make a triangle is 3.

We can select 3 non-collinear points out of 8 points in 8C3 ways

We can deduct the collinear points in 5C3 ways

Therefore, the number of triangles formed out of 8 points removing the possibility of selecting collinear points = 8C3 – 5C3 – 1