In the days when it was just postal entries I'm certain they didn't check through over 100000 envelopes every week - they'd just open a handful and check them until they'd found enough correct ones.
I'm not sure how they do it with multiple entry methods- maybe they pick a set number of each or maybe they have a random selection method. I suspect postal entries get less priority as they are a pain-maybe they go straight in the recycling bin - but I have no evidence