[herval]

> Let's take a small example. We have 20 bins. You are going to put 3 things in those bins, with each thing getting its own bin.

Now imagine a number of these bins _can hold zero things_ (not 3). Eg in a world where all bins are the same size, you can always steal 3 things from any of the bins, whereas in a world where the bin sizes vary. You'd hit a few bins which are guaranteed empty. Doesn't this directly affect the probabilities?