PHP Random Prize Giver with Parameters [on hold]

I'm struggling with where to start with this one.

Basically a client has 324 prizes they would like to 'randomly' give away over the course of four days. This works out to be around eight prizes every hour.

My question is, what would be the best way to go about 'fixing' this so that all of the prizes don't run out within the first hour yet are still all winnable?