Exam

BITSAT

Year

2016

Subject

Mathematics

Chapter

Permutation and Combination

BITSAT 2016 · Mathematics · Permutation and Combination

If three vertices of a regular hexagon are chosen at random, then...

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

Step-by-step solution

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