2014 AMC 10B Problem 10

In the addition shown below A, B, C, and D are distinct digits. How many different values are possible for D?

\begin{array}{lr}&ABBCB\\ +& BCADA\\ & DBDDD\end{array}

\textbf{(A) }2\qquad\textbf{(B) }4\qquad\textbf{(C) }7\qquad\textbf{(D) }8\qquad\textbf{(E) }9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.