+28 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
+357 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!
