**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}}

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