Question

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

• A. \(\dfrac13\)
• B. \(\dfrac15\)
• C. \(\dfrac1{10}\)
• D. \dfrac12

Hint:

In a regular hexagon, only alternate vertices form equilateral triangles.

Answer 1

The Correct Option is C

Step 1: Total ways =6\choose3=20.
Step 2: Favorable equilateral triangles =2. P=(2)/(20)=\frac110