Question

# In a convex hexagon, two diagonals are drawn at random. The probability that the diagonals intersect at an interior point of the hexagon, is

A
512
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B
712
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C
25
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D
None of these
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Solution

## The correct option is A 512In a convex hexagon there are 6 points.So total number of ways to join any two points =6C2Out of which there are 6 edges and rest are diagonals.∴ no of diagonals =6C2−6 =6!2!.4!−6 =15−6 =9.Out of 9 diagonals 2 diagonals can be chosen in 9C2=36 ways.Intersection will occur if two diagonal intersect i.e, if 4 points can joins.∴ Total number of intersections =6C4=15∴ The probability that diagonal intersect at an interior point =1536=512Hence, the answer is 512.

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