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45 lines
993 B
Python
45 lines
993 B
Python
# -.- coding: latin-1 -.-
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"""
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Combinatoric selections
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Problem 53
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There are exactly ten ways of selecting three from five, 12345:
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123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
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In combinatorics, we use the notation, 5C3 = 10.
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In general,
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nCr = n!/(r!(n−r)!),where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.
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It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
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How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater
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than one-million?
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"""
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from math import factorial
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def combinations(n, r):
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return factorial(n) / (factorial(r) * factorial(n - r))
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def solution():
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"""Returns the number of values of nCr, for 1 ≤ n ≤ 100, are greater than
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one-million
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>>> solution()
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4075
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"""
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total = 0
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for i in range(1, 101):
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for j in range(1, i + 1):
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if combinations(i, j) > 1e6:
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total += 1
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return total
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if __name__ == "__main__":
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print(solution())
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