Please break the solution into more steps to help me understand.

A large pool of adults earning their first driverís license includes 50% low-risk drivers,
30% moderate-risk drivers, and 20% high-risk drivers. Because these drivers have no
prior driving record, an insurance company considers each driver to be randomly selected
from the pool.
This month, the insurance company writes 4 new policies for adults earning their first
driverís license.
What is the probability that these 4 will contain at least two more high-risk drivers than
low-risk drivers?
(A) 0.006
(B) 0.012
(C) 0.018
(D) 0.049
(E) 0.073

Solution to be broken down further:

Solution: D
Let
X = number of low-risk drivers insured
Y = number of moderate-risk drivers insured
Z = number of high-risk drivers insured
f(x, y, z) = probability function of X, Y, and Z
Then f is a trinomial probability function, so

        
 4   3   3  2  2
Pr 2 0,0, 4 1, 0,3 0,1,3 0, 2, 2
0.20 4 0.50 0.20 4 0.30 0.20 4! 0.30 0.20
2!2!
0.0488

Here are the urls to the sample questions below:
http://www.soa.org/Files/Edu/edu-exam-p-sample-quest.pdf
http://www.soa.org/Files/Edu/edu-exam-p-sample-sol.pdf