Question

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. $\frac{3}{5}$

Answer 1

The correct option is D $\frac{3}{5}$

A regular 3 sided polygon is nothing else but a heptagon for creating isosceles triangle we need to choose adjacent sides only.

No. of ${△}^{\prime }s$ formed $=7C_3$

While number of isosceles triangle formed $=$ No. of points $\times$ points available $=7\times 3.$

$\Rightarrow$ So, probability $=\frac{7\times 3}{7C_3}=\frac{21}{35}=\frac{3}{5}.$

Hence, the answer is $\frac{3}{5}.$