from lib.memoize import memoize
from fractions import Fraction


def solve(balls=(2, 3, 4), target=30):

    nb_balls = sum(balls)

    @memoize
    def solve_(targets_):
        if sum(targets_) == 0:  # Toutes les balles ont étés tirées
            return 1
        # On tire une nouvelle balle
        ans = 0
        for b, t in enumerate(targets_):
            if t > 0:
                ans += Fraction(balls[b], nb_balls) * solve_(targets_[:b] + (t-1,) + targets_[b+1:])
        return ans

    return solve_((target,)*len(balls))


if __name__ == "__main__":
    ans = solve()
    print(ans)
    print(float(ans))