So, with the bin filling decisions, do we want hoe many ordered lists there are, or how many unordered sets there are?

Changing the order of the decisions doesn't make a new possible outcome. To calculate how many possible outcomes there are, we keep the decision order fixed.

So, we want combinations here.

The number of ways to fill a histogram bin to binheight appears to be (sampcount C binheight) popcount ^ (sampcount - binheight), but I'm not sure !