053_combinatoric_selections.hs

-- 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 MyLib_haskell

main::IO()
main = print $ length $ filter (>1000000) [ choose' n r | n <- [1..100], r <-[1..100], r<=n]