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In a convex hexagon two diagonals are dr...

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

`5//12`

B

`7//12`

C

`2//5`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
Number of diagonals of a hexagon `- .^(6)C_(2)-6=9`
Number of ways of selecting two diagonals `= .^(9)C_(2)=36`
Number of ways of selecting two intersecting diagonals
= Number of ways of selecting four vertices of the hexagon
`=.^(6)C_(4)=15`
Hence, required probability `=(15)/(36)=(5)/(12)`
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