In a card game with a single deck (no jokers), there are $52! = 8.1 * 10^{67}$ ways to order the deck. How many different ways are there for a game played by shuffling three such decks together?
I believe the answer to this question is fairly straightforward. The number of possible orderings would simply be $\frac{156!}{{3!}^{52}}$ if I am not mistaken since we have 3 of each card. Since the value of $52!$ was explicitly mentioned, I am assuming that it should be meaningfully incorporated into this equation somehow but I am not sure how to do it. Thanks and any insights will be well appreciated.