## Geometry: Common Core (15th Edition)

$792$
To evaluate a factorial expression, we multiply the number by each of the preceding integers until we get to $1$. We simplify the factorials in the numerator and in the denominator, and then divide: $\frac{12!}{5!7!}=\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{(5\times4\times3\times2\times1)(7\times6\times5\times4\times3\times2\times1)}=\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1}=792$