Geoffrey:

It is a source of fascination to me that you were able to come up with
a number for how many possible planner combinations there were for
each planner/solver example.
For example, where this kind of calculation comes from or how to derive my own ?

Example from Drools Solver Manual:

Set     # students      # exams/topics  # periods       # rooms #
possible solutions
exam_comp_set1  7883    607     54      7
1.11000574474221096210367623e+1052
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