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In a n- sided regular polygon, the proba...

In a `n-` sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is `(2^n C_2)/(^(^(n C_(2-n)))C_2)` b. `(^(n(n-1))C_2)/(^(^(n C_(2-n)))C_2)` c. `(^n C_4)/(^(^(n C_(2-n)))C_2)` d. none of these

A

`(2^(n)C_(2))/(.^((.^(n)C_(2-n)))C_(2))`

B

`(.^(n(n-1))C_(2))/(.^((.^(n)C_(2)-n))C_(2))`

C

`(.^(n)C_(4))/(.^((.^(n)C_(2)-n))C_(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
When 4 points are selected, we get one intersecting point. So, probability is
`(.^(n)C_(4))/(.^((.^(n)C_(2)-n))C_(2))`
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