Probability Problems

bodensee9

Hi

I was wondering if someone could check if I did these things correctly?

(a) How many ternary (0, 1, 2) sequences of length 10 are there without any pair of consecutive digits the same?

If you have 10 digits, so there are 3 choices for the 1st digit, and 2 digits for each later digit, so 3 * (2) ^ 9?

(b) there are 8 applicants for a job and 3 different judges who rank the applicants. applicants are chosen if each judge appear in the top 3 of all the different rankings of the judges. What's the probability that X will be chosen?

So there are (8!)^3 different rankings. And the different rankings possible with X as 1st, 2nd, or 3rd is 3 * 7!. So then this means that the probability that X is among the top three for 1 judge is (3 * 7!)/8!. And the probability that X will be among the top 3 for all the judges is ((3*7!)/8!)^3.

Thanks!!