from itertools import *

# probabilities of various events when drawing balls at random without
# replacement from a shuffled urn with r red and b blue balls
def red_blue(red, blue, k):
    total = 0
    no_red = 0
    at_least_one_red = 0
    one_of_each = 0
    same_number = 0
    for arrangement in combinations(range(red + blue), red):
        total = total + 1
        # count the number of red balls among the first k
        red_count = count_reds(arrangement, k)
        # update the counters depending on the value
        if red_count == 0:
            no_red = no_red + 1
        else:
            at_least_one_red = at_least_one_red + 1
            if red_count < k:
                one_of_each = one_of_each + 1
        if 2 * red_count == k:
            same_number = same_number + 1
    return (no_red * 1.0 / total, at_least_one_red * 1.0 / total, one_of_each * 1.0 / total, same_number * 1.0 / total)

# determine the number of red balls among the first k in an arrangement
def count_reds(arrangement, k):
    red_count = 0
    for pos in arrangement:
        if pos < k:
            red_count = red_count + 1
    return red_count