[gergery]

I’m new at this but
If the 9 are indistinguishable, then I’d think you would enumerate each case, then multiply by how those cases can occur.

So how can people get off the elevator?
9 people at one floor, no people at the other four floors (9,0,0,0,0)
8 people at one floor, 1 person at different floor (8,1,0,0,0)
7 people at one floor, 2 people at different floor (7,2,0,0,0)
7 people at one floor, 1 person at another floor (7,1,1,0,0)
etc, down to (2,2,2,2,1)

Then multiply each case by the ways it can be sorted –ie. pick.
(9,0,0,0,0) can be sorted in P(5,1) ways
(8,1,0,0,0) can be sorted in P(5,2) ways

Then add ‘em up.

Since the people are indistinguishable, you don’t need to then multiply by which people get off ie. (8,1,0,0,0) can be chosen C(9,8) ways.