You're example of Dice 1 has eight sides so the probability of;
If you role the dice three times, you multiple the probabilities together ie
probability of rolling A,A,B in 3 dice is
If you now have a side which is AA and this negates the effect of rolling an A ie you roll 3 dice AA,A,B then only the B is used then you use the same formula;
probability of rolling AA,A,B in 3 dice is
Does this help? What combinations are you attempting to calculate? A little more detail and I could help you build an excel spreadsheet to work everything out.