Question

If four of eight vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed is a rectangle(not a square), is

• A. $\frac{1}{15}$
• B. $\frac{2}{25}$
• C. $\frac{2}{35}$
• D. $\frac{7}{45}$

Answer 1

The correct option is C $\frac{2}{35}$


Total number of quadrilaterals possible $={}^8{C}_4=70$
and total number of rectangles $=4$
So, required probability $=\frac{n\left(A\right)}{n\left(S\right)}=\frac{4}{70}=\frac{2}{35}$