number of posts per page + random + exclude categories

pre_get_posts in your child themes functions file is the best in my opinion.

add_action( 'pre_get_posts', 'wpsites_custom_get_posts' );

function wpsites_custom_get_posts( $query ) {

if( $query->is_main_query() && $query->is_home() ) {

$query->set( 'cat', '-182,-184' );

$query->set( 'posts_per_page', '12' );

$query->set( 'orderby', 'RAND' );
    }
}

This method is more flexible in my opinion.