In a `n-` sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is: (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

Options

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

Answer

C

Explanation

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