question_answer

If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

A) \[\frac{1}{8}\]                      

B) \[\frac{2}{21}\]

C) \[\frac{1}{32}\]                                  

D) \[\frac{1}{35}\]

Correct Answer: D

Solution :

By the diagram only 2 rectangles are formed ADEH, GFCB.

\[\therefore \] number of favourable cases = 2

Total number of cases \[{{=}^{8}}{{C}_{4}}\]

\[\therefore \]  required probability \[=\frac{2}{^{8}{{C}_{4}}}=\frac{1}{35}\]