Problem 15: Lattice paths

Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.

How many routes are there through a 2020 grid?

Solution: 

This can be solved with Dynamic programming, Brute force and, Combinatorics , I've used 

combinatorics because it's the fastest way to do this.

Here's the java code for it:

public class Prob15 {

public static void main(String args[])
{

int gridSize = 20;
long path =1;

for(int i=0 ; i < gridSize ;i++)
{
 path *= 2*gridSize-i;
 path /= (i+1);
 }
System.out.println(path);
}

 }