"""
There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

In combinatorics, we use the notation, 5C3 = 10.

In general,

nCr =
n!/r!(n−r)!
,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.
It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.

How many, not necessarily distinct, values of  nCr, for 1 ≤ n ≤ 100, are greater than one-million?
"""


def factorial(x):
    if x == 0:
        return 1
    elif x > 0:
        return factorial(x - 1) * x


def combinations(n, r):
    return int(factorial(n) / (factorial(r) * factorial(n - r)))


if __name__ == '__main__':

    count = 0
    for n in range(0, 101):
        for r in range(0, n):
            if combinations(n, r) > (10 ** 6):
                count += 1

    print(count)
    print(combinations(23, 10))
