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Bunuel
There are 5 line segments of lengths 2, 3, 4, 5 and 6 cm. What is the probability that three randomly chosen line segments cannot form a triangle?

A. 1/5
B. 3/10
C. 2/5
D. 1/2
E. 7/10


Are You Up For the Challenge: 700 Level Questions
Total number of ways of selecting 3 lines from the 5 lines provided is 5C3 = 10
The lines chosen will not form a triangle when the sum of any two lines is not greater than the third line.
3 selections fall into this category : {2,3,5}, {2,3,6} and {2.4.6}.
Required probability = 3/10.
Answer choice B­
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Bunuel
There are 5 line segments of lengths 2, 3, 4, 5 and 6 cm. What is the probability that three randomly chosen line segments cannot form a triangle?

A. 1/5
B. 3/10
C. 2/5
D. 1/2
E. 7/10

The triplets that cannot form a triangle = {(2, 3, 5), (2, 3, 6), (2, 4, 6)} = 3
So, Probability that a triangle cannot be formed = 3/10

Option B
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5 segments of 2,3,4,5 and 6

To not form a triangle
Case 1=> 2,3,5 or 2,3,6
Case 2 => 2,4, 6

3+4 =7 All cases are valid
3+5 = 8
4+5 = 9
5+6 = 11

So only 3 possibilities
Total = 5C3 = 10

Probability = 3/10
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