BITSAT2016MathematicsPermutation and CombinationActual
If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is:
Options
- A1 3
- B1 5
- C1 10
- D1 2
Correct answer
C. 1 10
Step-by-step solution
Three vertices can be selected in ⁶ C ₃ ways. The only equilateral triangles possible are A ₁ ~A ₃ ~A ₅ and A ₂ ~A ₄ ~A ₆ p = 2 ⁶ C ₃ = 2 20 = 1 10