Card probability question

I am having trouble with a exam review question. The question is

How many 5 card poker hands are there? what is the probability of a hand containing 3 aces and 2 queens?

For the first part there are $\displaystyle 52 \choose{5}$ possible hands

For the second part I am getting something like this

$\displaystyle 13 \choose{1}$$\displaystyle 4 \choose{3}$$\displaystyle 12 \choose{1}$$\displaystyle 4 \choose{2}$ / $\displaystyle 52 \choose{5}$

Is this correct? Thanks for any help that anyone can provide.