Answer the Question $\mathrm { n }$ Is Large $\mathrm { n }$

Multiple Choice

Answer the question.
-Many calculators or computers cannot directly calculate 70 ! or higher. When $\mathrm { n }$ is large, $\mathrm { n }$ ! can be approximated by $\mathrm { n } ! = 10 ^ { \mathrm { K } }$ , where $\mathrm { K } = ( \mathrm { n } + 0.5 ) \log \mathrm { n } + 0.39908993 - 0.43429448 \mathrm { n }$ . Evaluate 78 ! using the approximation given above.

A) $1.151 \times 10 ^ { 2 }$
B) $1.131 \times 10 ^ { 115 }$
C) $1.281 \times 10 ^ { 114 }$
D) $3.356 \times 10 ^ { 308 }$