How can I create a jotform where there is a limited number of registration spots available?

I would like to create several jotforms where customers can choose which event to sign up for, but each event has limited quantity.

is it possible to limit the number of registrations? 

Yes, that is possible. You can set the Form Status to Disable on Submission limit in the Form Settings page. Here's how:

Open your form and go to the Settings page. Click the Form Settings tab and click the drop down menu of the Form Status then select the Disable on submission limit. After that, you can now set how many submission limit you want to your form and customize the Warning message once the limit is reached.

Let us know if you need further help. Thank you.