advancement condition

I have an advancment (rare collector) when a player collects 5 specific 'Rare items'. one advancement when a player collects a specific 15 'uncommon' items and another advancement when a player collects 30 specific 'common' items. I want to give another advancement when all three of these are done. I couldn't work this out, is this possible, to trigger an advancement once a collection of advancements are made. if so how?