#### Answer

$_{8}$P$_{4}$ is greater

#### Work Step by Step

You have $_{10}$P$_{3}$ and $_{8}$P$_{4}$ .Solve in order to determine which is greater:
A:
$_{10}$P$_{3}$=$\frac{10!}{(10-3)!}$ -simplify-
$_{10}$P$_{3}$=$\frac{10!}{7!}$ -write using factorial-
$_{10}$P$_{3}$=$\frac{10*9*8*7*6*5*4*3*2*1}{7*6*5*4*3*2*1}$ -simplify-
$_{10}$P$_{3}$=720
B:
$_{8}$P$_{4}$=$\frac{8!}{(8-4)!}$ -simplify-
$_{8}$P$_{4}$=$\frac{8!}{4!}$ -write using factorial-
$_{8}$P$_{4}$=$\frac{8*7*6*5*4*3*2*1}{4*3*2*1}$ -simplify-
$_{8}$P$_{4}$=1680
$_{8}$P$_{4}$ is greater