Hi, Susan. Thanks for getting in touch about the functionality available in WooCommerce Tickets. It does indeed sounds like WooCommerce Tickets would be a good solution based on your description.
You can see the add-on in action on our demo site:
http://wpshindig.com/event/the-events-calendar-wootickets-wordpress-demo/
For a taste of what it will be like to manage inventory, I recommend you download the (free) WooCommerce plugin and give it a test drive. You’ll find the inventory management under the WooCommerce Products section in the Dashboard.
Are there any other questions I can answer to help you evaluate the add-on?