three of the six vertices of regular hexagon are chosen at random.the possibility that the triangle with three vertices is equilateral equals

three vertices can be chosen as 6C3 after that what to do

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- Mar 3rd 2011, 08:41 PMprasumregular hexagon
three of the six vertices of regular hexagon are chosen at random.the possibility that the triangle with three vertices is equilateral equals

three vertices can be chosen as 6C3 after that what to do - Mar 4th 2011, 02:08 AMprasum
i think we can take central angle of regular hexagon and by angle in a segment=half central angle we can judge whether the triangle is equilateral or not

- Mar 4th 2011, 05:04 AMSoroban
Hello, prasum!

I don't suppose you made a sketch . . .

Quote:

Three of the six vertices of regular hexagon are chosen at random.

Find the probability that the three vertices form an equilateral triangle.

Three vertices can be chosen as 6C3. . Right!

After that, what to do?

. . $\displaystyle \begin{array}{ccccc}

&& A \\

F &&&& B \\ && * \\

E &&&& C \\

&& D \end{array}$

There are onlyequilateral triangles: .$\displaystyle ACE$ and $\displaystyle BDF.$*two*