MYSQL Select One Random record from each Category

I have a database with an Items table that looks something like this:

id
name
category (int)

There are several hundred thousand records. Each item can be in one of 7 different categories, which correspond to a categories table:

id
category

I want a query that chooses 1 random item, from each category. Whats the best way of approaching that? I know to use Order By rand() and LIMIT 1for similar random queries, but I've never done something like this.

Solution 1:

This query returns all items joined to categories in random order:

SELECT
c.id AS cid, c.category, i.id AS iid, i.name
FROM categories c
INNER JOIN items i ON c.id = i.category
ORDER BY RAND()

To restrict each category to one, wrap the query in a partial GROUP BY:

SELECT * FROM (
    SELECT
    c.id AS cid, c.category, i.id AS iid, i.name
    FROM categories c
    INNER JOIN items i ON c.id = i.category
    ORDER BY RAND()
) AS shuffled_items
GROUP BY cid

Note that when a query has both GROUP BY and ORDER BY clause, the grouping is performed before sorting. This is why I have used two queries: the first one sorts the results, the second one groups the results.

I understand that this query isn't going to win any race. I am open to suggestions.