I was thinking, this is like putting 9 indistinguishable balls into 3 distinguishable boxes where every box must have one ball. Once you put a ball in each box then we have two but 6 balls into 3 boxes. We can use stars (are the balls) and bars (the box dividers). For example this |**||****, would be 2-0-4. So that's the same as 9C3=84.