-- 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?

import Euler

n `nCr` r = product [max r (n-r) + 1 .. n] `div` product [1 .. min r (n-r)]
main = print $ length [ () | n <- [1..100], r <- [1..n], n `nCr` r > 1000000 ]