Giving my users all a blog

Try WPMU (WOrdPress Multi-User) here:

https://mu.www.ads-software.com

Your web host must support wildcard DNS, and virtual hosts must be enabled. It’s tricky to get running on Dreamhost but it can be done.

What WPMU does is set up a master WP site (the original installation) and allows users to register for their own WP blogs with the following structure:

username.yourdomain.com

Several WPMU communities that I know of off the top of my head are WordPress.com, iblogs.com and blogsome.com.

Good luck.

If you are a teacher, there is also edublogs.org and if you are a student, uniblogs.org

I would like for them to have a blog in the format of..

https://www.domainname.com/Blogs/UserID

possible with wordpress?

Unless you install a WP for every “userID” – no.
Wordpress is not a multiblog system. Please, take a look at the https://mu.www.ads-software.com – as it was suggested above.