053.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

#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?

#Answer:
	#4075

from time import time; t=time()

M = 1000000
s = 0
for n in range(23, 101):
    c = n
    for r in range(2, n//2+1):
        c = c*(n+1-r)//r
        if c > M:
            s += n+1-2*r
            break
print(s)#, time()-t