91Ó°ÊÓ

To do this, we can use the counting principle, which states that if one event can occur in m ways and a second event can occur in n ways, then the number of ways both events can occur is m*n. In this case, each die can fall in one of 6 possible ways, so the total number of different ways they can fall is: \(6 * 6 = 36\) So, there are 36 different ways the dice can fall.

We can create a list of all possible outcomes and track the combinations where the sum equals nine. An efficient way to approach this is by listing the combinations one die at a time: Dice 1 rolls a 1: (1,8) - Not possible, as the highest number on the second die is 6. Dice 1 rolls a 2: (2,7) - One combination; 2 + 7 = 9. Dice 1 rolls a 3: (3,6) - One combination; 3 + 6 = 9. Dice 1 rolls a 4: (4,5) - One combination; 4 + 5 = 9. Dice 1 rolls a 5: (5,4) - One combination; 5 + 4 = 9. Dice 1 rolls a 6: (6,3) - One combination; 6 + 3 = 9. No other combinations have a sum of nine, as rolling a 7 or higher on the first die will result in a sum greater than nine. Based on the list above, there are 4 combinations that will result in a sum of nine. To summarize: - There are 36 different ways the dice can fall. - Out of these, 4 ways will give a sum of nine.