Get mixed category random posts

I whipped this up:

echo '<ul>';
    the_random_posts();
echo '</ul>';

/**
 * Send random posts to the browser (STDOUT).
 */
function the_random_posts() {

    // Use your own category ids.
    $random_posts = array_merge(
        get_random_posts( 31, 3 ),
        get_random_posts( 11, 1 ),
        get_random_posts( 24, 1 )
    );

    foreach ( $random_posts as $post ) {
        // Change this line to code you want to output.
        printf( '<li><a href="https://wordpress.stackexchange.com/questions/110170/%s">%s</a></li>', get_permalink( $post->ID ), get_the_title( $post->ID ) );
    }
}

/**
 * Get $post_count random posts from $category_id.
 *
 * @param int $post_count Number of random posts to retrieve.
 * @param int $category_id ID of the category.
 */
function get_random_posts( $category_id, $post_count ) {

    $posts = get_posts( array(
        'posts_per_page' => $post_count,
        'orderby'        => 'rand',
        'cat'            => $category_id,
        'post_status'    => 'publish',
    ) );

    return $posts;
}

If any posts are in 2 or more of the selected categories there is a chance that a post will be repeated (like a post that is in both category A and category B). A static variable with an array of previously retrieved post might fix that.

This algorithm prints the posts in the order they were called.

get_random_posts( 31, 3 ), // First, 3 random posts from Category A
get_random_posts( 11, 1 ), // Then,  1 random post  from Category B
get_random_posts( 24, 1 )  // Then,  1 random post  from Category C

If you want a random list, shuffle $random_posts.