question_answer

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is:

A) \[\frac{1}{3}\]

B) \[\frac{1}{5}\]

C) \[\frac{1}{10}\]

D) \[\frac{1}{2}\]

Correct Answer: C

Solution :

[c] Three vertices can be selected in \[^{6}{{C}_{3}}\] ways. The only equilateral triangles possible are \[{{A}_{1}}{{A}_{3}}{{A}_{5}}\] and \[{{A}_{2}}{{A}_{4}}{{A}_{6}}\] \[p=\frac{2}{^{6}{{C}_{3}}}=\frac{2}{20}=\frac{1}{10}\]