Group categories, etc.

Basically I’d like to group categories, but let me explain.

Say you have three drop down menus stacked vertically with a submit button underneath in a sidebar or what have you.

Each drop down menu contains a group of different unique categories.

When creating a WordPress Post you would add one category from each of the three drop down menus to it.

Once you select a category from all three drop down menus on the live site, you click the submit button. On the next page or below after clicking submit, it would show all the posts that match all three categories.

I hope that makes sense, any idea on how to start the drop down thing would be awesome. It’s fairly easy to make a drop down menu show a category, but two or more and mixing them as above is where I’m stuck.