Question 1096462: Assume you are rolling two dice; the first one is red, and the second is green. Use a systematic listing to determine the number of ways you can roll a total less than 9 on the two dice.
Answer by greenestamps(13198)   (Show Source):
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If the red die shows 1, then any of the 6 numbers on the green die will make a sum of less than 9:
R,G = 1,1 or 1,2 or 1,3 or 1,4 or 1,5 or 1,6 --> 6 ways
If the red die shows 2, then still any of the 6 numbers on the green die will make a sum of less than 9:
R,G = 2,1 or 2,2 or 2,3 or 2,4 or 2,5 or 2,6 --> 6 ways
If the red die shows 3, then now only 5 of the 6 numbers on the green die will make a sum of less than 9:
R,G = 3,1 or 3,2 or 3,3 or 3,4 or 3,5 --> 5 ways
If the red die shows 4, then now only 4 of the 6 numbers on the green die will make a sum of less than 9:
R,G = 4,1 or 4,2 or 4,3 or 4,4 --> 4 ways
If the red die shows 5, then now only 3 of the 6 numbers on the green die will make a sum of less than 9:
R,G = 5,1 or 5,2 or 5,3 --> 3 ways
And if the red die shows 6, then now only 2 of the 6 numbers on the green die will make a sum of less than 9:
R,G = 6,1 or 6,2 --> 2 ways
The total number of ways to get a sum less than 9 is
6+6+5+4+3+2 = 26
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