Depending on your required effect
(MySQL)
mysql_query("SELECT topic from news_articles ORDER BY RAND() LIMIT 3");
But the above will randomize all and pick the three. I think if you need to just randomize the last 3 sorted records then you will probably have to do it in php itself.
or if you want to sort the randomized records you can do:
mysql_query("SELECT topic from news_articles ORDER BY RAND(), {$strSortfield} LIMIT 3");
Where $strSortfield is the field you want to sort the result table in. Putting the $strSortfield before the RAND() will not give you the needed effect because the sort will happen first and the randomize function will not fire.