Probability - Finding Daily Doubles

Any help would be appreciated.

There are 3 clues labeled "daily double" on the game show Jeopardy. If three equally matched contenders play, what is the probability that:
1) A single contestant find all 3 daily doubles
2) The returnnig champion gets all 3 daily doubles
3) Each of the players selects precisly one of the daily doubles

1 and 2) Let's say Moe is one of the contestants. The chance that he will get all 3 daily doubles is (1/3)^3.

So the chance that any one of the three contestants will get all 3 is 3 x (1/3)^3.

Thanks for your help! My instructor advised that part 1 is (1/3)^2; part 2 you were correct and 3) is (2/3)(1/3). They only response that makes sense, to me anyway, is no. 2.