#-.- 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)