Question

There are five lines of length 1, 3, 5, 7, 9. Take randomly three straight segments from those five lines. Calculate the probability that the three selected segments can form a triangle

Answer 1

• 3/10 or 30%

Explanation:

Given the segments:

• 1, 3, 5, 7, 9

Number of combinations of 3 line segments out of 5:

• 5C3 = 5!/3!2! = 10

Triangle can be formed if only any side is smaller than the sum of the other two sides.

Possible triangles:

• (3,5,7), (3,7,9) and (5,7,9) - the number is 3

Probability:

• Favorable outcomes/total outcomes = 3/10 or 30%