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Dakota randomly selected three different integers 1 through 6 What is the probability that the three numbers selected could be the sides of a triangle? Express your answer as a common fraction.

the answer btw is not 17/28

 Jul 2, 2020
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Hey I'm back yippee

 

The number of ways to get 3 integers is 6c3=20

 

A triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers... but only when the sum of any 2 selected numbers is greater than the third number.

 

 Cases possible when the longest side of the triangle is 6: 

(6, 5, 4), (6, 5, 3), (6, 5, 2), (6, 4, 3)

 

Cases possible when the longest side of the triangle is 5:

(5, 4, 3), (5, 4, 2)

 

Cases possible when the longest side of the triangle is 4: 

(4, 3, 2)

 

4+2+1=7

 

So we get 7/20 as our answer.

 

Yay!

 Jul 2, 2020

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