Project Euler 15 - Lattice Paths

'''
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.
'''

# The solution is a string made up with 40 letters, but we have to use
# exactly 20 '0's ---> right move and exactly 20 '1's ---> down move
# So, we have n = 40 letters and two teams with n1 = 20 letters and n2 = 20
# To produce all the combinations, I use the formula: combinations = n! / (n1! * n2!),
# where n = n1 + n2

def factorial(n):
    if n < 0 or n != int(n):
        print("Error using the factorial function.")
        return -1000
    elif n == 0 or n == 1:
        return 1
    else:
        fact = list()
        fact.append(1)
        for i in range(1, n+1):
            fact.append(i * fact[i-1])
        return fact[n]


def produceCombinationsOfTwoTeams(n, n1, n2):
    if n == n1 + n2 and n == int(n) and n1 == int(n1) and n2 == int(n2) and n > 0 and n1 > 0 and n2 > 0:
        return factorial(n) / factorial(n1) / factorial(n2)
    else:
        print("Error using the fucntion produceCombinationsOfTwoTeams")
        return -1000

# MAIN FUNCTION
print(produceCombinationsOfTwoTeams(40, 20, 20))