I would like to know what the rule is to explain why we do not use the genitive construction hotel's room. Instead, we say "a hotel room".
- a hospital bed
- a bike stand
Would it suffice to ask "What kind of..."?
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Your examples use nouns that are used to modify other nouns (attributive nouns). Possessive (also called Saxon Genitive) constructions, on the other hand, show possession [in the extended (my bike's front wheel) rather than just the proprietorial (John's bike) sense].
"a hotel's room" - a room belonging to a hotel
"a hotel room" - a specific type of room, somehow related to hotels (in this case also usually belonging to the hotel but that is not necessarily important)
similarly "hospital's bed", vs "hospital bed"
"the bike's stand" would imply that the stand belongs to the bike while "bike stand" describes a type of stand that is somehow related to bikes (of course, here, designed to house bikes).