Drawing multiple prizes - All at once or one at a time?

[pokeMATHter]

If I knock out a Tag Team Pokemon, and get to draw 3 prize cards, do I draw then all at once or one at a time?

I can imagine a situation where some of my prize cards are face up, but I may want to draw a face down card or two before deciding to take a face up card.

 

[PokePop]

I don't know of any requirement that you announce which three prizes you are drawing before you actually do.
The act of drawing the prize will allow you to see it, so it could influence your choice of remaining prizes.