Question : In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is
(A) 2\dfrac{nC_{2}}{\left( nc_{2}-2\right) C_{2}}
(B) \dfrac{n(n-1)C_{2}}{\left( nc_{2}-n\right) C_{2}}
(C) \dfrac{nC_{4}}{\left( nc_{2}-2\right) C_{2}}
(D) none of these
Answer : option (C)
Solution :
When 4 points are selected, we get one intersecting point. So, probability is \dfrac{nC_{4}}{\left( nc_{2}-2\right) C_{2}}