It would be great to have an additional product field for Quantity Available.
For example, we are using it for class registration and there are 15 spots available. When all 15 have been selected in customer responses, that class is closed/no longer available for others to sign up.
How about this solution?
There are other solutions on that site to show the number of tickets left, and others to give you more control over the ticket sales (inventory) but I think this one will work for the scenario you outlined above.