#-.- coding: latin-1 -.-
from __future__ import print_function
from math import factorial
'''
Combinatoric selections
Problem 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?
'''
try:
xrange #Python 2
except NameError:
xrange = range #Python 3
def combinations(n, r):
return factorial(n)/(factorial(r)*factorial(n-r))
total = 0
for i in xrange(1, 101):
for j in xrange(1, i+1):
if combinations(i, j) > 1e6:
total += 1
print(total)