query_post random posts then sort by category

Hello,

I currently have my wordpress set to display 50 of over 1000 posts. What I’d like to do is use query post to first call up a random selection of posts, then reorganize those posts by category…so i will have called up 50 random posts, grouped by category. this is for the home page, and for FULL POSTS, not a list.

it seems like it would be easy to do…except i cannot find any orderby values that would group by category, nor do i know how to use it in conjuction with orderby=rand

i’m thinking of something like the following:

<?php if (have_posts()) : ?>
<?php query_posts('orderby=rand,category_id'); ?>
<?php while (have_posts()) : the_post(); ?>

if anyone can help, please! thanks!