Probability - Matching terms and definitions question

I wondered whether I was on the right track with regard to the following question:

A student has to match three terms that she has never seen before with their definitions. If she guesses, what is the probability of her

- Getting all three correct?
- Getting none correct?
- Getting exactly one correct?
- Getting exactly two correct?

What assumptions did you make? Do they seem reasonable?

**Hint:** List the sample space.

Using numbers to represent definitions and letters to represent terms, I think the sample space should be as follows:

A1 B1 C1

A2 B2 C2

A3 B3 C3

If we say that A3, B3 and C3 are correct, these are my tentative answers:

probability of getting 1 correct is 3/9,

probability of getting 2 correct is P(1correct) * P(1 correct) = 9/81 =1/9

probability of getting all 3 correct is P(1correct) * P(1 correct)* P(1correct) = 27/729 = 1/27

I am not sure about how to approach the probability of getting none correct.

1 minus P(1correct) ie 1-3/9 is a possibility but it may be more complicated than this. Any advice on how to approach this and comments on my tentative answers would be much appreciated.