The cubes at the right are each numbered 1 through 6. During a game, both are rolled and the faces landing up are added. How many ways can a person playing the game roll a sum less than 8?

Question

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Answer 1

2 cubes, each with 6 sides, numbered 1 through 6

how many ways can you roll them both and get a sum less than 8?

possible sums are

2 which happens only 1 way 1+1

3 two ways 1+2 and 2+1

4 three ways 1+3, 3+1 and 2+2

5 four ways 1+4, 4+1, 2+3, 3+2

6 five ways 1+5, 5+1, 2+4, 4+2, 3+3

7 six ways 1+6, 6+1, 2+5, 5+2, 3+4, 4+3

count the ways: 1+2+3+4+5+6+7 = 7(7+1)/2 (by Gaus' formula n(n+1)/2 or just add them) = 28 ways

8 five ways

9 four ways

10 three ways

11 two ways

12 one way

total 36 ways

28/36 = 7/9 = 77 7/9 % chance of getting less than 8