# Number of ways to go from one point to another in a grid

• Difficulty Level : Easy
• Last Updated : 16 Apr, 2021

Given the NxN grid of horizontal and vertical roads. The task is to find out the number of ways that the person can go from point A to point B using the shortest possible path.
Note: A and B point are fixed i.e A is at top left corner and B at bottom right corner as shown in the below image. 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.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

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In the above image, the path shown in the red and light green colour are the two possible paths to reach from point A to point B.
Examples:

```Input: N = 3
Output: Ways = 20

Input: N = 4
Output: Ways = 70```

Formula:
Let the grid be N x N, number of ways can be written as. How does above formula work?
Let consider the example of the 5×5 grid as shown above. In order to go from point A to point B in the 5×5 grid, We have to take 5 horizontal steps and 5 vertical steps. Each path will be an arrangement of 10 steps out of which 5 steps are identical of one kind and other 5 steps are identical of a second kind. Therefore
No. of ways = 10! / (5! * 5!) i.e 252 ways.

## C++

 `// C++ implementation of above approach``#include ``using` `namespace` `std;` `// function that will``// calculate the factorial``long` `factorial(``int` `N)``{``    ``int` `result = 1;``    ``while` `(N > 0) {``        ``result = result * N;``        ``N--;``    ``}``    ``return` `result;``}` `long` `countWays(``int` `N)``{``    ``long` `total = factorial(N + N);``    ``long` `total1 = factorial(N);``    ``return` `(total / total1) / total1;``}` `// Driver code``int` `main()``{``    ``int` `N = 5;``    ``cout << ``"Ways = "` `<< countWays(N);``    ``return` `0;``}`

## Java

 `// Java implementation of above approach``class` `GfG {` `    ``// function that will``    ``// calculate the factorial``    ``static` `long` `factorial(``int` `N)``    ``{``        ``int` `result = ``1``;``        ``while` `(N > ``0``) {``            ``result = result * N;``            ``N--;``        ``}``        ``return` `result;``    ``}` `    ``static` `long` `countWays(``int` `N)``    ``{``        ``long` `total = factorial(N + N);``        ``long` `total1 = factorial(N);``        ``return` `(total / total1) / total1;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `N = ``5``;``        ``System.out.println(``"Ways = "` `+ countWays(N));``    ``}``}`

## Python3

 `# Python3 implementation of above approach` `# function that will calculate the factorial``def` `factorial(N) :``    ` `    ``result ``=` `1``;``    ` `    ``while` `(N > ``0``) :``        ` `        ``result ``=` `result ``*` `N;``        ``N ``-``=` `1``;``    ` `    ``return` `result;` `def` `countWays(N) :` `    ``total ``=` `factorial(N ``+` `N);``    ``total1 ``=` `factorial(N);``    ` `    ``return` `(total ``/``/` `total1) ``/``/` `total1;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``N ``=` `5``;``    ` `    ``print``(``"Ways ="``, countWays(N));` `# This code is contributed by Ryuga`

## C#

 `// C# implementation of above approach``using` `System;``class` `GfG``{` `    ``// function that will``    ``// calculate the factorial``    ``static` `long` `factorial(``int` `N)``    ``{``        ``int` `result = 1;``        ``while` `(N > 0)``        ``{``            ``result = result * N;``            ``N--;``        ``}``        ``return` `result;``    ``}` `    ``static` `long` `countWays(``int` `N)``    ``{``        ``long` `total = factorial(N + N);``        ``long` `total1 = factorial(N);``        ``return` `(total / total1) / total1;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String []args)``    ``{``        ``int` `N = 5;``        ``Console.WriteLine(``"Ways = "` `+ countWays(N));``    ``}``}` `// This code is contributed by Arnab Kundu`

## PHP

 ` 0)``    ``{``        ``\$result` `= ``\$result` `* ``\$N``;``        ``\$N``--;``    ``}``    ``return` `\$result``;``}` `function` `countWays(``\$N``)``{``    ``\$total` `= factorial(``\$N` `+ ``\$N``);``    ``\$total1` `= factorial(``\$N``);``    ``return` `(``\$total` `/ ``\$total1``) / ``\$total1``;``}` `// Driver code``\$N` `= 5;``echo` `"Ways = "``, countWays(``\$N``);``    ` `// This code is contributed by ajit``?>`

## Javascript

 ``
Output:
`Ways = 252`

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