Problem 15 : Lattice paths

Problem Statement

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 20×20 grid?

Solution

def paths(n,k):
    from math import factorial,sqrt
    return int(factorial(n)/(factorial(k)*factorial(n-k)))

print(paths(20+20,20))

Output

137846528820