If $n$ and $k$ are positive integers, then how many ordered pairs $(n, k)$ satisfy $n!+8=2^k?$

If $n$ and $k$ are positive integers, then how many ordered pairs $(n, k)$ satisfy $n!+8=2^k?$

A. 0
B. 1
C. 2
D. 3
E. Infinitely many

Answer: C

Source: GMAT Club Tests

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