Question

Three of the six vertices of a regular hexagon are chosen the random. What is the probability that the triangle with these vertices is equilateral. A. `(1)/(10)` B. `(1)/(5)` C. `(3)/(10)` D. `(3)/(20)` Select the correct answer from above options

Answer 1

Correct Answer - A Since, there is a regular hexagon, then the number of ways of choosing three vertices is `^6C_3` And, there is only two ways i.e. choosing vertices of a regular hexagon alternate, here`A_1,A_3,A_5 or A_2,A_4,A_6` wiil result in an equilateral triangle. `therefore" Required probility `therefore` Required pobability `=2/(""^(6)C_3)=2/((6!)/(3!3!))=(2xx3xx2xx3xx2)/(6xx5xx4xx3xx2xx1)=1/10`