Stirling's Formula (Named After Scottish Mathematician, James Stirling: 1692-1770) Is $n ! \approx \sqrt { 2 \pi n } \left( \frac { n } { e } \right) ^ { n }$

Multiple Choice

Stirling's formula (named after Scottish mathematician, James Stirling: 1692-1770) is used to
approximate large values of n!. Stirling's formula is $n ! \approx \sqrt { 2 \pi n } \left( \frac { n } { e } \right) ^ { n }$ a. Use Stirling's formula to approximate the given expression. Round to the nearest whole unit.
b. Compute the actual value of the expression.
- $8 !$

A) a. 39,902
b. 40,312
B) a. 40,111
b. 40,320
C) a. 40,111
b. 40,312
D) a. 39,902
b. 40,320