How to assign different categories to pages in wordpress?

You can create a page template (for service page) and then set it to particular page, on which you want to display posts.

After that open page template and paste below code where you wan to show posts.

<?php
query_posts('cat=1'); // cat=1 , id of category you want to show (e.g. cat id of food category )
while (have_posts()) : the_post(); // loop for posts with category id = 1 
the_content(); // print content of all founded posts
endwhile; // end loop.
?>

Refer this for more help