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

[Gmat_mission]

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