1. The problem statement, all variables and given/known data Now, this problem is not the typical stars and bars problem. I'm actually trying to solve for this: If I had n red marbles and m blue marble, I want the probability that I pick n red marbles and only 1 blue marble. The order is irrelevant, meaning, the only thing that is required is that after I have picked n+1 marbles, I had exactly n red marbles and 1 blue marble. How do I do this? 2. Relevant equations (Number of possibilities for picking 1 marble and n red marbles)/(Total number of possiblities) = the probability 3. The attempt at a solution So, I thought of it like this. I have n+1 open little crates (distinct boxes), and n indistinct objects (my red marbles). I am looking for the amount of ways to organize my n red marbles into n+1 crates, with the restriction that none of the crates can have more than one marble in it. By doing this, I can find the ways that I can pick exactly n marbles and leave one empty crate. This is basically the same thing as finding the ways that I can pick n marbles and 1 blue marble, although I am not really taking into account the amount of ways I can choose from the m blue marbles. I'm actually looking for a general way to find the amount of ways that I could organize n red marbles and k blue marbles in n+k slots, where each slot has exactly one item. Is there already a general formula for this? Thanks!