Probability Question 326

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

Options:

A) $ \frac{2{}^{n}C_2}{{}^{({}^{n}C_2-n)}C_2} $

B) $ \frac{^{n(n-1)}C_2}{{}^{({}^{n}C_2-n)}C_2} $

C) $ \frac{^{n}C_4}{{}^{({}^{n}C_2-n)}C_2} $

D) none of these

Show Answer

Answer:

Correct Answer: C

Solution:

When 4 points are selected, we get one intersecting point. So , probability is $ \frac{^{n}C_4}{^{{{(}^{n}}C_2-n)}C_2} $