Solution to Problem 53

Project Euler/Problem 53/sol1.py

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+#-.- 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)