Dynamically update a page from entries

I am trying to create a sign-up form for volunteer positions. I would like that form to dynamically populate a page that lists the available volunteer spots so that potential volunteers can see what is available for them to do.

More context - I work for a church and on any given Sunday we need several people to help with worship services. For example we would need 4 ushers, 2 communion servers, and 1 reader. I would like to create a form and page in wordpress that allows people to sign up, and then dynamically updates the page to show who is serving as ushers, servers, readers, etc. At the same time it would be great to have those options removed from the form when they are filled.

Is there a way to do this?