2003 Cayley Problem 24

In how many ways can a, b, c, and d be chosen from the set \{0, 1, 2, ..., 9\} so that a < b < c < d and a + b + c + d is a multiple of three?

\textbf{(A)}\ 54\quad \textbf{(B)}\ 64\quad \textbf{(C)}\ 63\quad \textbf{(D)}\ 90\quad \textbf{(E)}\ 72

If there are no answer choices shown, enter a numerical answer.

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