Cómo usar la función Rand combinada con Union en MySQL

Podría crear un SQL externo donde la cláusula from sea una especie de tabla temporal como esta:

 SELECT food_name from (
  SELECT foodName
  FROM food
  WHERE foodCategory_id = 1 OR 2
  ORDER BY RAND() limit 1) a
 UNION
 SELECT food_name from (
  SELECT foodName
  FROM food
  WHERE foodCategory_id = 7 OR 8 OR 9
  ORDER BY RAND() limit 1) b
 UNION
 SELECT food_name from (
  SELECT foodName
  FROM food
  WHERE foodCategory_id = 10 OR 11
  ORDER BY RAND() limit 1) c