\textbf{154-} The number of ordered triples, with non-negative integer and non-positive integer coordinates, such that the sum of every three coordinates of each set equals $10$ and each coordinate is less than $6$, is which of the following?
$$17 \ (1) \hspace{2cm} 18 \ (2) \hspace{2cm} 20 \ (3) \hspace{2cm} 21 \ (4)$$
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