How many ordered pairs of sets $(A, B)$ have the properties:

1. $ A\subseteq \{1, 2, 3, 4, 5, 6\} $
2. $ B\subseteq\{2, 3, 4, 5, 6, 7, 8\} $
3. $ A\cap B $ has exactly $3$ elements.

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