Jackpot probablity There are two parts to a problem:
Part (a);
In a Lottery, three white balls are drawn (at random) from twenty balls numbered 1 through 20, and a blue SuperBall is drawn (at random) from ten balls numbered 21 through 30. When you buy a ticket, you select three numbers from 1-20 and one number from 21-30. To win the jackpot, the numbers on your ticket must match the three white balls and the SuperBall. (You don't need to match the white balls in order).
If you buy a ticket, what is your probability of winning the jackpot?
Part (b):
In a Lottery, three white balls are drawn (at random) from twenty balls numbered 1 through 20, and a blue SuperBall is drawn (at random) from ten balls numbered 21 through 30. When you buy a ticket, you select three numbers from 1-20 and one number from 21-30. To win a prize, the numbers on your ticket must match at least two of the white balls or must match the SuperBall.
If you buy a ticket, what is your probability of winning a prize?
Approach for part (a):
Here is how I am solving the problem.Since 3 number in white balls needs to match during the first pick, the probability is 3/20. For the second one it will be 2/19 and 3rd one 1/18. That combined with probability for blue ball will be 3/20 * 2/19 * 1/18 * 1/10
part (b):
3 cases (1) only blue ball matches and no match in white balls (2) no match in blue ball but 2 out of 3 white ball matches (3) Both matches
Probability for case (a): 
1/10 * 17/20 * 16/19 * 15/18
case (b) :
9/10 * 3/20 * 2/19
case (c) :
1/10 * 3/20 * 2/19 * 1/18
Add case (a) + (b) + (c) because they are mutually exclusive.
Am I correct in my approach?

Part (a) is fine !
Part (b) can be solved using only 2 cases: 
(i) succeed with white balls, fail with blue ball [ best to use combinations here ]
(ii) succeed with blue ball
$$\text{Indicated Pr = }\left[\dfrac{{3\choose 2}{17\choose 1} + {3\choose 3}}{20\choose 3} \times\dfrac{9}{10}\right] + \dfrac{1}{10} =\approx 0.1411$$
