"""
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

counter1 = 0
counter2 = 0
for i in range(23,101):
    for j in range(1, math.ceil(i * 0.5) + 1):
        if int(math.factorial(i) / (math.factorial(j) * math.factorial(i - j))) > 1000000:
            if i / j >= 2:
                counter1 += 1
            else:
                counter2 += 1

print(2 * counter1 + counter2)
