Exam

JEE Main

Year

2019

Date

12 April

Shift

Morning Shift

Subject

Mathematics

Chapter

Permutation and Combination

JEE Main 2019 · 12 April · Morning Shift · Mathematics · Permutation and Combination

If three of the six vertices of a regular hexagon are chosen at...

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:

Step-by-step solution

Total number of ways of selecting three points from vertices of a regular hexagon

$= {C}_{3} 6 = \dfrac{6.5 . 4}{1.2 . 3} = 20$
Favorable selection (forming equilateral triangle)
$= 2\left(ACE, BDF\right)$
$⇒$ Required probability $P = \dfrac{Numberoffavourableselections}{Totalselections}$
$= \dfrac{2}{20} = \dfrac{1}{10}$