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?

There is another way to find part a
This problem could be rephrased in math as $P(three\ white\ balls\ and\ blue\ Superball)$. There are $\binom{20}{3}=1140$ possibilities for three balls and $10$ possibilities for the Superball, which is $1140\cdot10=11400$ total possibilities. And there is only one way to get the ticket, so it is $\boxed{\frac{1}{11400}}$
Second way:
There is $20\cdot19\cdot18\cdot10$ total ways, and there is $3\cdot2\cdot1\cdot1$ ways for Superball and the three white balls. Total probability is $\frac{3\cdot2\cdot1\cdot1}{20\cdot19\cdot18\cdot10}$ which simplifies to $\boxed{\frac{1}{11400}}$
