> Can somebody explain why not just make a die with 5! sides, and roll it once to decide the order?

Hey, that’s a good idea—now we just need to decide who rolls the die. …Well, if we had a set of die that each player could roll one of, and the highest number rolled gets to roll the 120-sided die. Of course, we’d have to ensure that there’s no chance of a tie.

Hmm… this idea has legs…