AMC 10 2020b Problem 19

In a certain card game, a player is dealt a hand of $10$ cards from a deck of $52$ distinct cards. The number of distinct (unordered) hands that can be dealt to the player can be written as $158A00A4AA0$. What is the digit $A$? $\textbf{(A) } 2 \textbf{(B) } 3 \textbf{(C) } 4 \textbf{(D) } 6 \textbf{(E) } 7$