A handful means either the amount you can hold in your hand "add a handful of salt", or a small number so "Country X only has a handful of aircraft carriers" is

A handful means either the amount you can hold in your hand "add a handful of salt", or a small number so "Country X only has a handful of aircraft carriers" is fine. I think with apples it would be the second meaning but it's a grey area. With something smaller like "a handful of cherries" I'd go with the amount that can be held.