Question

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three

vertices is equilateral, is equal to

• A. $\frac { 1 } { 2 }$
• B. $\frac { 1 } { 5 }$
• C. $\frac { 1 } { 10 }$
• D. $\frac { 1 } { 20 }$

Answer 1

Answer: (C)

$\frac { 1 } { 10 }$

Answer 2

Total number of triangles which can be formed

=${ } ^ { 6 } C _ { 3 } = \frac { 6 \times 5 \times 4 } { 1 \times 2 \times 3 } = 20$Number of equilateral triangles = 2.

\ Required probability $= \frac { 2 } { 20 } = \frac { 1 } { 10 }$ .