Multiple themes under the same wordpress installation

Using WP as a CMS, is it possible to do the following?

Say you design a web site and you have two category systems to serve two different audiences. One audience is women, the other audience is general.

You want to provide two distinct look and feel for these two different audience groups. When FOR WOMEN link is clicked at the home page, the next page uses a say Theme1 and categories are drastically different and if you were to NOT click on the FOR WOMEN link on the home page, you would be presenting your site with THEME2 and with a whole different category system. It’s like running two different WP sites but I want one login to be able to get in. I’m new to WP, I don’t know if you can have different themes for various sections for your WP site.

Could someone offer a way?