Say we have 198 people who can be seated across 30 tables. Each table can sit 7, 6 or 5 people.
We don't care about the order of people within a table, and we don't care about the order of the tables, so a change to either of those won't represent a new valid combination. Any move of an individual outside of their table constitutes a new valid combination.
How many combinations can we have?
I need to code this into Python and am struggling to express it.
My working so far is:
There are 7 different grouping combinations of 5,6 and 7 to make 198.
For each grouping combination we need to move person 1 to available seat 1 then move person 2 to each available seat and for each available seat for person 2 we move person 3 to each available seat etc etc it cascades.
However my understanding is that it would be diminishing cascade as person n increases, the more people have been sat for that combination and therefore the number of remaining available seats decreases. Does this miss anything?