Math Help - 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

1. Getting all three correct?
2. Getting none correct?
3. Getting exactly one correct?
4. 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.

I think you have defined your sample space incorrectly, you say that A3, B3 and C3 are correct, that means that all 3 terms are matched to the same definition?

also , I think it would be impossible to get *exactly* 2 correct.

There are ways to do the matchings.
In only one of those does she get all three correct.
There two ways to get none correct.

So think again.