Questions: Assume two six-sided dice are rolled each with the numbers 1,2,3,4,5, and 6. The first one is red and the second one is green. Use a systematic listing to determine the number of ways to roll a total less than 10 on the two dice. How many ways are there to roll a total of less than 10 ? ways

Solution Steps

When two six-sided dice are rolled, each die has 6 possible outcomes. Therefore, the total number of possible outcomes is \( 6 \times 6 = 36 \).

List all possible combinations of the red and green dice, where the first number represents the red die and the second number represents the green die: \[ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), \\ (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), \\ (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), \\ (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), \\ (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), \\ (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). \]

From the list above, count the number of combinations where the sum of the two numbers is less than 10: \[ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), \\ (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), \\ (3,1), (3,2), (3,3), (3,4), (3,5), \\ (4,1), (4,2), (4,3), (4,4), (4,5), \\ (5,1), (5,2), (5,3), (5,4), \\ (6,1), (6,2), (6,3). \] There are 30 such combinations.

\[ \boxed{30} \]

Final Answer