Question

How many 4 card hands that contain exactly 3 aces and 1 queen can be chosen from a 52 card deck?

Answer 1

There are 16 possible hands.

Choosing 3 aces from 4 possible is expressed by:
$_4C_3=\frac{4!}{3!1!} = 4$

Choosing 1 queen from 4 possible is expressed by:
$_4C_1=\frac{4!}{1!3!}=4$

This gives us 4*4 = 16 possible hands.