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

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

When 4 points are selected, we get one intersecting point. So, probability is $\dfrac{nC_{4}}{\left( nc_{2}-2\right) C_{2}}$