# Number of triangles formed from a set of points on three lines

Given three integers m, n and k that store the number of points on lines l1, l2 and l3 respectively that do not intersect. The task is to find the number of triangles that can possibly be formed from these set of points.

Examples:

```Input: m = 3, n =  4, k = 5
Output: 205

Input: m = 2, n =  2, k = 1
Output: 10
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• The total number of points are (m + n + k) which must give number of triangles.
• But ‘m’ points on ‘l1’ gives combinations which cannot form a triangle.
• Similarly, and number of triangles can not be formed.
• Therefore, Required Number of Triangles = Below is the implementation of the above approach:

## C++

 `// CPP program to find the possible number ` `// of triangles that can be formed from ` `// set of points on three lines ` `#include ` `using` `namespace` `std; ` ` `  `// Returns factorial of a number ` `int` `factorial(``int` `n) ` `{ ` `    ``int` `fact = 1; ` `    ``for` `(``int` `i = 2; i <= n; i++) ` `        ``fact = fact * i; ` `    ``return` `fact; ` `} ` ` `  `// calculate c(n, r) ` `int` `ncr(``int` `n, ``int` `r) ` `{ ` ` `  `    ``return` `factorial(n) ` `           ``/ (factorial(r) * factorial(n - r)); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `m = 3, n = 4, k = 5; ` `    ``int` `totalTriangles ` `        ``= ncr(m + n + k, 3) ` `          ``- ncr(m, 3) - ncr(n, 3) - ncr(k, 3); ` `    ``cout << totalTriangles << endl; ` `} `

## Java

 `//Java  program to find the possible number  ` `// of triangles that can be formed from  ` `// set of points on three lines  ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `     `  `// Returns factorial of a number  ` `static` `int` `factorial(``int` `n)  ` `{  ` `    ``int` `fact = ``1``;  ` `    ``for` `(``int` `i = ``2``; i <= n; i++)  ` `        ``fact = fact * i;  ` `    ``return` `fact;  ` `}  ` ` `  `// calculate c(n, r)  ` `static` `int` `ncr(``int` `n, ``int` `r)  ` `{  ` ` `  `    ``return` `factorial(n)  ` `        ``/ (factorial(r) * factorial(n - r));  ` `}  ` ` `  `// Driver code  ` `     `  `    ``public` `static` `void` `main (String[] args) { ` ` `  `        ``int` `m = ``3``, n = ``4``, k = ``5``;  ` `        ``int` `totalTriangles = ncr(m + n + k, ``3``) -  ` `           ``ncr(m, ``3``) - ncr(n, ``3``) - ncr(k, ``3``);  ` `        ``System.out.println (totalTriangles);  ` `         `  `         `  `    ``} ` `} `

## Python 3

 `# Python 3 program to find the  ` `# possible number of triangles  ` `# that can be formed from set of  ` `# points on three lines ` ` `  ` `  `# Returns factorial of a number ` `def` `factorial(n): ` `    ``fact ``=` `1` `    ``for` `i ``in` `range``(``2``, n ``+` `1``): ` `        ``fact ``=` `fact ``*` `i ` `    ``return` `fact ` ` `  `# calculate c(n, r) ` `def` `ncr(n, r): ` ` `  `    ``return` `(factorial(n) ``/``/` `(factorial(r) ``*`  `                             ``factorial(n ``-` `r))) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``m ``=` `3` `    ``n ``=` `4` `    ``k ``=` `5` `    ``totalTriangles ``=` `(ncr(m ``+` `n ``+` `k, ``3``) ``-`  `                      ``ncr(m, ``3``) ``-` `ncr(n, ``3``) ``-`  `                      ``ncr(k, ``3``)) ` `    ``print``(totalTriangles) ` ` `  `# This code is contributed  ` `# by ChitraNayal `

## C#

 `// C# program to find the possible number  ` `// of triangles that can be formed from  ` `// set of points on three lines  ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `// Returns factorial of a number  ` `static` `int` `factorial(``int` `n)  ` `{  ` `    ``int` `fact = 1;  ` `    ``for` `(``int` `i = 2; i <= n; i++)  ` `        ``fact = fact * i;  ` `    ``return` `fact;  ` `}  ` ` `  `// calculate c(n, r)  ` `static` `int` `ncr(``int` `n, ``int` `r)  ` `{  ` ` `  `    ``return` `factorial(n) / (factorial(r) *  ` `                           ``factorial(n - r));  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main ()  ` `{ ` `    ``int` `m = 3, n = 4, k = 5;  ` `     `  `    ``int` `totalTriangles = ncr(m + n + k, 3) -  ` `                         ``ncr(m, 3) - ncr(n, 3) - ` `                         ``ncr(k, 3);  ` `                          `  `    ``Console.WriteLine (totalTriangles);  ` `} ` `} ` ` `  `// This code is contributed  ` `// by anuj_67.. `

## PHP

 `

Output:

```205
```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.