"""
EP - 53

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?
"""

import math

def binomial(n,r):
    # This function computes nCr
    assert 0 <= r <= n
    return math.factorial(n) // (math.factorial(r) * math.factorial(n-r))

def compute():
    total = 0
    for n in range(1,101):
        for r in range(1,n):
            if binomial(n,r) > 1000000:
                total += 1
    return total

if __name__ == "__main__":
    print('Values of nCr > one million is {}'.format(compute()))
