Hi Nella,
Thanks for getting in touch. There isn’t a way to restrict availabily with our core plugin (The Events Calendar). However, we do have several ticketing plugins that allow users to register for your event, making it easy for you to restrict the number of people.
You can check out our ticketing plugins on their product page. I also recommend that you read about the new plugins coming with our 4.0 release next month. We are releasing a new free ticketing plugin with basic RSVP functionality which might meet your needs. We’ll also have a more robust premium tickets plugin available.
Let me know if you have any further questions!
Best,
Leah