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If 3 different integers are randomly selected from the set {

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If 3 different integers are randomly selected from the set {

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If 3 different integers are randomly selected from the set {1, 2, 3, 4, 5, 6}, what is the probability that a triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers?

A) 0.25
B) 0.3
C) 0.35
D) 0.40
E) 0.45

Source: www.gmatprepnow.com
Difficulty level: 650-ish
Answer: C

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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\(= 7/20=0.35\)

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