A fair die is rolled three times. What is the probability that the first outcome is less than (and not equal to) the second outcome, and the second outcome is less than (and not equal to) the third outcome?

For part (a), first consider the simple case where we roll two dice. What is the probability that the second roll is greater than the first? Assuming a six-sided dice, the total number of outcomes $ (i, j) $ is $6^2$.