Question

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

• A. $\frac{1}{7}$
• B. $\frac{1}{3}$
• C. $\frac{3}{7}$
• D. $\frac{3}{5}$

Answer 1

Answer: (D)

We have,
Regular Heptagon from vertices ‘$A$’ There are three isosceles triangle formed
$AED,AFC,AGB$
Similarly, from other vertices also formed three isosceles triangle
$\therefore$ Required probability $=\frac{7\times 3}{{}^7{C}_3}$
$=\frac{7\times 3\times 1\times 2\times 3}{7\times 6\times 5}$
$=\frac{3}{5}$