Thread:Project:Support desk/Linking to a random page within a specified category

I have created a large wiki of information that uses a series of topical categories. Someone can use a category as an interest (say, of "Category:History, American Revolution" or "Category:Architecture, Gothic Revival").

As each of these categories has a number of entries (such as a long list of historical properties that are designed in the Gothic Revival style).

A am looking for a way that someone can specify the category, then receive a random page only within that category. So if someone is interested in pages dealing with Gothic Revival architecture, they will only see pages within Category:Architecture, Gothic Revival.

Is there any way of doing this?