Every key is randomly drawn individually. The program Vicarious wrote will put each of your choices into the respective key pool, and you will have a fair chance at receiving each choice that you receive. Starting from your first choice down, once you've won your max you will be withdrawn.
To answer your question, if you choose a LE Mayhem as your first choice, and you are not chosen, it will move down your choices until you hit your max. Potentially you could receive nothing if none of your choices are drawn.
We've tried to make it as absolutely fair as possible.