[SmartBlondeGPhB]

If you are asked to prefs, you will be somewhere on that house's bid list but you are not guaranteed a bid at that house. Most PNM's go to more than one house for prefs but they can only get one bid, so they can't be guaranteed a bid from more than one house.

And if a sorority has 2 pref parties with 40 girls at each party and quota is 50, well obviously they can't give bids to all the women.

I'll let the more knowledgeable among us give a more technical answer on bid matching.