On Sun, May 30, 2021, 5:58 PM Karl <[1]gmkarl@gmail.com> wrote:

   On Sun, May 30, 2021, 5:52 PM Karl <[2]gmkarl@gmail.com> wrote:

   (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.

   Goal: validate expression.  Note: expression is useful on computer, not
   mailing list.

   We can break the outcomes into sets based on which of the decisions are
   the ones that pick the bin of interest.  This is a selection of
   sampbinheight decisions from among sampcount total decisions, which
   cannot be reordered.  (sampcount C sampbinheight).
   Each of these sets has the same two unknown spaces, none of which
   overlap, of which non-relevent decisions are made, and which of the
   popbinheight samples are selected.  The non-relevent decisions are made
   from a nondepleting group that is (popcount - popbinheight) large.  The
   sample choices are each made from a homogenous group that is
   popbinheight large.  Selecting a different item from popbinheight is a
   different decision, the same way selecting a different nonrelevent item
   is ... I think?
   So we have (popcount - popbinheight) ^ (sampcount - sampbinheight) and
   we have popbinheight ^ sampbinheight .
   These are the same expressions listed above.
   I'm sure I made another error, but I don't know what it is, and it's
   nice to have a better guess.

   Remember to simulate to find more mistakes.

References

   1. mailto:gmkarl@gmail.com
   2. mailto:gmkarl@gmail.com