Nate, Ben, Suzy, and Gracie play bridge. In how many ways can the 52-card deck be dealt so that each player receives 13 cards?

Since all cards are being dealt, wouldn't this just be $\displaystyle \left(52\right)_{52}$?

My reasoning is that in the 52! permutations of the cards each player can just get every fourth card, so it doesn't matter about the 13 card hands. It only matters in how many ways all 52 cards can be selected from the deck.