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

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++

`// 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; ` `} ` |

## Java

`// 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)); ` ` ` `} ` `} ` |

## Python3

`# 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 ` |

## C#

`// 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. ` |

## PHP

`<?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. ` `?> ` |

**Output:**

4

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