Solver for probabilistic coupons problem

gistfile1.hs

import Data.Ratio

main :: IO ()
main = print $ result 5

result :: Integer -> Rational
result size = abs $ sum
  [ fromIntegral mult * infTailSum size d
  | (mult, d) <- coeffs size
  ]

coeffs :: Integer -> [(Integer, Rational)]
coeffs size =
  [ ( ((-1) ^ i) * choose (size - 1) i, i % size)
  | i <- [1 .. size - 1]
  ]

infTailSum :: Integer -> Rational -> Rational
infTailSum size d = infiniteSum - partialSum where
  infiniteSum = 1 / ((1 - d) ^ 2)
  partialSum = sum [ (i%1) * d ^ (i - 1) | i <- [1 .. size - 1]]

choose :: Integer -> Integer -> Integer
choose n k = fact n `div` (fact (n - k) * fact k)

fact :: Integer -> Integer
fact n = product [1 .. n]