'''
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, 
.

In general, 
 
, where , , and .

It is not until , that a value exceeds one-million: 
.

How many, not necessarily distinct, values of 
 for , are greater than one-million?
 '''
# Okay I have to admit that it looks really bad without the math equations

import time
import math


def main():
    print("Hello, this is Patrick")
    t0 = time.time()

    tooBig = 1000000
    counter = 0

    for n in range(1, 101):
        for r in range(1, n+1):
            if math.comb(n, r) > tooBig:
                counter += 1
    
    print(counter, time.time() - t0)

if __name__ == "__main__":
    main()