Number of ways to select 3 integers from the set\(= 6C3=20\)

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

1. Cases possible when the longest side of the triangle is 6
\((6,5,4), (6,5,3), (6,5,2), (6,4,3)\)

2. Cases possible when the longest side of the triangle is 5
\((5,4,3), (5,4,2)\)

3. Cases possible when the longest side of the triangle is 4
\((4,3,2)\)

Total number of cases possible\(= 4+2+1=7\)

Probability\(= 7/20=0.35\)