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-- 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?
main = do
print (length [pascal n r | n <- [1..100], r <- [1..n], pascal n r > 1000000])
pascal :: Integer -> Integer -> Integer
pascal _ 0 = 1
pascal n k = (pascal n (k - 1)) * (n + 1 - k) `div` k
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