First Day Assignment: Too Eager

I begin my time as a FT analyst in two weeks. Last week we met with our staffer, who informed us that she has four projects to give out on the first day, to be distributed randomly among the ten of us new incoming analysts.

She claims that the distribution will be random, but should I specifically ask for one of these projects or hint heavily that I want one to try to get a "leg up" on the first day? Or should I just let her choose as she wishes as to not seem over eager? Does it even matter if I don't get one of these projects and have to wait it out for a week or two before I get my first assignment?

Thx for looking. Feel free to PM me.