Can someone check this for me? (Equivalence classes)

[StuperSting]

Question: Find the equivalence classes and the number of equivalence classes of the following relations.

A is the set of all possible strings of 3 or 4 letters in alphabet {A, B, C, D}, and (x, y) ∈ R if and only if x and y have the same first letter and the same third letter.
My attempted answer: A_B_, A_C_, A_D_, B_A_, B_C_, B_D_, C_A_, C_B_, C_D_, D_A_, D_B_, D_C_.
This would be 12 different classes.

Is this correct or am I missing something?

 

[gopher_p]

There is typically no restriction on strings containing repeat letters. Other than that, this looks fine.

 

[StuperSting]

Awesome thanks :)