Project Euler 205 (0.7 s)

pr205.hs

import Control.Monad (replicateM, join)
import Data.List (nub, sort, group)
import Control.Arrow ((&&&), (***))
import Numeric (showFFloat)

allVariantsNumber :: Integer
allVariantsNumber = 4^9 * 6^6

groupVariants :: [[Integer]] -> [(Integer,Integer)]
groupVariants = map ((&&&) head (toInteger . length)) . group . sort . map sum

peterVariants :: [(Integer, Integer)]
peterVariants = groupVariants $ replicateM 9 [1..4]

colinVariants :: [(Integer, Integer)]
colinVariants = groupVariants $ replicateM 6 [1..6]

peterWins :: Integer
peterWins = sum [ pVariantNumbers * cVariantNumbers | (pSum, pVariantNumbers) <- peterVariants, (cSum, cVariantNumbers) <- colinVariants, pSum > cSum ]

probability :: Double
probability = uncurry (/) . join (***) fromIntegral $  (peterWins, allVariantsNumber)

main = print $ showFFloat (Just 7) probability ""