#!/usr/bin/python
import random
import itertools

# the set of sets of letters on each card
s = [['A','B','C'], ['D','E','F','G'], ['H','I','J','K','L']]

# the deck of all possible cards
deck = list(itertools.product(*s))

# the full sequence of letters in the entire deck
allchars = set(list(itertools.chain.from_iterable(s)))


# Monte Carlo iteration size
samplingsize = 1000000

# iterate through multiple hand sizes
print "sampling size = ", samplingsize
for k in xrange(5, 41):

    # the size of the hand
    handsize = k

    # count the number of hands that were a success
    handsuccess = 0

    for j in xrange(0, samplingsize):

        thishand = []
        for i in xrange(0,handsize):
            # pick a card at random, insert it into hand
            thishand.append(deck[random.randint(0,len(deck) - 1)])

        # get all unique chars in this hand
        thishandchars = set(list(itertools.chain.from_iterable(thishand)))

        # compare the unique chars of the hand with the unique chars of the deck
        if(thishandchars == allchars):
            # hand contains all letters in deck
            handsuccess += 1;

    print "For a hand size of {}, probability = {:.3f}%".format(handsize, 100.0 * handsuccess / samplingsize)