TITLE: Why is a simulation of a probability experiment off by a factor of 10?
QUESTION [9 upvotes]: From a university homework assignment:
There are $8$ numbered cells and $12$ indistinct balls. All $12$ balls are randomly divided between all of the $8$ cells. What is the probability that there is not a single empty cell ($i.e.$ each cell has at least $1$ ball)?
The answer is $\large\frac{\binom{11}{7}}{\binom{19}{7}}$ which is about $0.0065$. I reached this result independently, and it was confirmed by the official homework solution of the university.
A friend of mine and I independently wrote Python simulations that run the experiment many times (tested up to $1,000,000$). We used both Pythons' random generator and several randomly generated lists from www.random.org. Results were similar and consistently hovering around $0.09$ which is a factor of $10$ or even a bit more off from the expected theoretical result.
Have we made some wrong assumptions?
Any ideas for this discrepancy?
P.S.: Here is the Python code that I wrote, and maybe there is some faulty logic there.
def run_test():
    global count, N

    def run_experiment(n_balls, n_cells, offset):
        cells = [0] * n_cells
        # toss balls randomly to cells:
        for j in range(n_balls):
            cells[random.randrange(0, n_cells)] += 1
            # cells[int(lines[offset + j])] += 1
        cells = sorted(cells)
        # print(cells)

        # check if there is an empty cell. if so return 0, otherwise 1:
        if cells[0] == 0:
            return 0
        return 1

    count = 0
    N = 1000000
    offset = 0
    N_CELLS = 8
    N_BALLS = 12
    # iterate experiment
    for i in range(N):
        result = run_experiment(N_BALLS, N_CELLS, offset=offset)
        count += result
        offset += N_CELLS

    print("probability:", count, "/", N, "(~", count / N, ")")

REPLY [2 votes]: The original problem is posed, so far as I can tell, to show the difference between combinations and permutations.  In nature, there is no such thing as indistinguishable balls.   Semi-infinite tests (e.g. Las Vegas) have shown this to be true.   
Now, if the problem really wants you to use "indistinguishable" balls for the purposes of solving the problem, then yes, you need to use combinations and not permutations when calculating all the ways the indistinguishable balls are placed into the containers.
And of course, you need to use permutations for the numbered balls, as they are distinguishable from each other and from the collection of indistinguishable balls.  
Now, I believe that Chris Culter's calculations reflect this difference.  Whether your Python code does this correctly we can't say until we see the code.