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# -.- coding: latin-1 -.-
"""
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?
"""
from math import factorial
def combinations(n, r):
return factorial(n) / (factorial(r) * factorial(n - r))
def solution():
"""Returns the number of values of nCr, for 1 ≤ n ≤ 100, are greater than
one-million
>>> solution()
4075
"""
total = 0
for i in range(1, 101):
for j in range(1, i + 1):
if combinations(i, j) > 1e6:
total += 1
return total
if __name__ == "__main__":
print(solution())