(popbinheight^sampbinheight) (popcount - popbinheight) ^ (sampcount -
   sampbinheight) (sampcount C sampbinheight)

   Is the combinations still looking ok, now that the system is describsd
   differently?

   The question is whether or not the expression counts all the possible
   different decision sets, without duplication, that result in exactly
   sampbinheight samples from popbinheight population portions.
   Remember to simulate to find more mistakes.