Thread: general encryption functions / block ciphers

So I've taken a stab at this question but am not sure if I am taking the right direction...

(1) The question is: how many possible encryption functions are there for a block cipher with block length 2 with plaintext and ciphertext consisting of sequences of elements from Z/2Z (i.e. a sequence of 1's and 0's).

So, I'm thinking that the plaintext of block 2 can only have 4 possibilities (0, 0) (0, 1) (1, 0) and (1, 1), and these are also the same possibilities for the ciphertext. There would be 4! = 24 mapping possibilities, and therefore 24 possible encryption functions?