Euler #121

import itertools
probability = 0
wins = list(itertools.product([0, 1], repeat=15))
wins = [x for x in wins if list(x).count(1) > 7]
for x in wins:
    disks, running = 2, 1
    for y in x:
        if y == 0:
            running *= (disks - 1)
        running /= disks
        disks += 1
    probability += running
print(1/probability)