“Hi. Do you have any vacancies?”
You had to travel to another city at the last minute. You don't have a hotel reservation, so you go to a hotel and ask this at the reception desk.
Hi. Do you have any vacancies?
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any (something)
The words "some" and "any" have almost the same meaning. But you use "some" in positive sentences:
He didn't study at a four-year university, but he does have some formal training.
"Any" is used in negative sentences like this:
It's also used in questions, like:
Is there any tea left?
(a hotel) has vacancies
If a hotel has rooms which are available for people to rent now, you can say that the hotel "has vacancies".
Some hotels have a neon sign out front which says "vacancies" if there are rooms available, and "no vacancies" if all of the rooms are full.