Remember to simulate to find more mistakes.
   (popbinheight^sampbinheight) (popcount - popbinheight) ^ (sampcount -
   sampbinheight) (sampcount C sampbinheight)
   I'm thinking that if we wanted to consider the number of samplings that
   made the whole precise histogram, we would replace the larger exponent
   with further copies of the rest of the expression, where sampcount is
   reduced appropriately in each.
   Is there an error, because popcount is not present in the result?  Not
   sure.  Popcount is needed to know the probability of getting one of the
   bins, but we are already assuming that we got them all ....