euler53.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, ^(5)C_(3) = 10.

In general,
^(n)C_(r) = 	
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: ^(23)C_(10) = 1144066.

How many, not necessarily distinct, values of  ^(n)C_(r), for 1 ≤ n ≤ 100, are greater than one-million?-}


import Shared(factorial)

euler53 = length [0 | n <- [1..100], r <- [1..100], r <= n, (factorial n)/((factorial r) * (factorial (n-r))) > 1000000]

main = print euler53