When catering an affair if there’s no eruv can the goyim take out the garbage?
They should not be asked to take out the garbage, because it involves an issur d’rabonon, and a hired waiter is considered a sechir yom, (a hired worker) and not a kablan (a contractor) who can choose to do the job after shabbos. If however he decided to do it on his own, you don’t have to stop him from doing it. Additionally if he is told, “The place needs to be cleaned up”, and he on his own takes the garbage out, without you telling him, you don’t have to stop him.
Have a good Shabbos
O:Ch 334-25, The Sanctity of Shabbos pg. 100,