Four fair dice are rolled. What is the probability of getting two different pairs?
I basically used the multiplication rule here: the first die can have $6$ possible outcomes, while the second one can have only $5$. The last two can only have one outcome each because they have to match the numbers on the first and second dice. Hence the numerator becomes $6 \cdot 5 \cdot 1 \cdot 1$. Then I divided by all possible outcomes, which is $6^4$. So the probability $= 30/6^4 = .023$.