Question

Assume a class has 17 members.

Answer 1

A) 4080
B) 6188

A is a permutation, since order would matter:
$P(17, 3)=\frac{17!}{(17-3)!}=\frac{17!}{14!}=4080$

B is a combination, since order does not matter:
$_{17}C_5=\frac{17!}{5!12!}=6188$