Multiple seperated categories on single page

I am about to set up a new site using WP, and was wondering if it is possible to have multiple categories on a single page, each displaying the latest post in that category?

So, for example I might have something like:

MAIN BLOG:

– Post 3 (category 1)
– Post 2 (category 1)
– Post 1 (category 1)

LATEST UPDATE:

– Post 1 (category 2)

LATEST NEWS:

– Post 1 (category 3)

So that if I post up something new to category 1, it will show up in the ‘MAIN BLOG’ section of the home page, but if i were to post something new to category 2, it would show up in the specified div in the ‘LATEST UPDATE’ section on the home page.

Does that make sense?