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                                                                         [AMU 1999]

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

B)            \[\frac{2}{21}\]

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

D)            \[\frac{1}{35}\]

Correct Answer: D

Solution :

                   Here only 2 rectangles are formed ADEH, GFCB.                    \ Number of favourable cases = 2                    and total number of cases \[{{=}^{8}}{{C}_{4}}\]                    \ Required probability                    = \[\frac{2}{^{8}{{C}_{4}}}\]\[=\frac{1}{35}\].