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Dakota randomly selected three different integers 1 through 8. What is the probability that the three numbers selected could be the sides of a triangle? Express your answer as a common fraction.

 Oct 16, 2022
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8 C 3 ==56 combinations

 

(2, 3, 4) , (2, 4, 5) , (2, 5, 6) , (2, 6, 7) , (2, 7, 8) , (3, 4, 5) , (3, 4, 6) , (3, 5, 6) , (3, 5, 7) , (3, 6, 7) , (3, 6, 8) , (3, 7, 8) , (4, 5, 6) , (4, 5, 7) , (4, 5, 8) , (4, 6, 7) , (4, 6, 8) , (4, 7, 8) , (5, 6, 7) , (5, 6, 8) , (5, 7, 8) , (6, 7, 8) , Total =  22 combinations meet the condition for 3 sides of a triangle.

 

Therefore, the probability is: 22 / 56 == 11 / 28

 Oct 17, 2022

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