question_answer

Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form the vertices of an isosceles triangle is

A)  \[\frac{1}{7}\]                                  

B)  \[\frac{1}{3}\]

C)  \[\frac{3}{7}\]                                  

D)  \[\frac{3}{5}\]

Correct Answer: D

Solution :

 \[\Delta AGB,\]\[\Delta \,AFC\]and\[\Delta \,AED\]are isosceles \[P=\frac{{}^{7}{{C}_{1}}\times 3}{{}^{7}{{C}_{3}}}=\frac{7\times 3}{\frac{7\times 6\times 5}{3\times 2}}=\frac{3}{5}\]