Your pairs are OK. Each pair has an equiprobability to be gotten.
The probability that the first dice yields X (for example 1) is 1/6. The probability that the second dice yields Y (for example 2) is 1/6.
Hence, the probability of getting the given pair (X,Y) is (1/6)*(1/6)=1/36
Among the 36 possible pairs, only 6 are the ones you're interested in.
Therefore, the probability of getting one of the 6 given pairs is 6/36=1/6.
Do you understand ?