If $a, b,$ and $c$ are digits for which \[ \begin{array}{cccc} & 7 & a & 2 \\ - & 4 & 8 & b \\ \hline & c & 7 & 3 \end{array} \] then find the value of $a + b + c$.

Let's think step by step and output the final answer within \boxed{}.
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