import collections

days = {'monday', 'tuesday', 'wednesday', 'thursday',
        'friday', 'saturday', 'sunday'}
events = {'A', 'B', 'C'}

def flip():
    answers = dict()
    for a_day in days:
        answers[a_day] = dict()
        for an_event in events:
            answers[a_day][an_event] = False

    for a_day in random.sample(days, 3):
        answers[a_day]['A'] = True

    for a_day in random.sample(days, 4):
        answers[a_day]['B'] = True

    for a_day in random.sample(days, 2):
        answers[a_day]['C'] = True

    multiple_days = 0
    for a_day in days:
        if collections.Counter(answers[a_day].values())[True] > 1:
            multiple_days = multiple_days + 1
    return multiple_days


def test():
    multiple_days = 0
    for x in range(1, 100000):
        v = flip()
        multiple_days = v + multiple_days
    print(multiple_days / (7.0 * 100000))