geometry help?

Question

If three different points are selected randomly from 6 equally spaced points on a circle, what is the probability that the triangle formed by connecting these three ponts will be equilateral.

Answer 1

Name the 6 points:
A, B, C, D, E, F

there needs to be three to make a triangle:
ABC
ABD
ABE
ABF
ACD
ACE
ACF
ADE
ADF
AEF
BCD
BCE
BCF
BDE
BDF
BEF
CDE
CDF
CEF
DEF

Possible Outcomes: 20
When you try drawing the equilateral triangles, only 2 of the possible 20 are actually equilateral, so
probability= 2/20 => 1/10

Answer 2

This is a simple probability problem; unfortunately, probability always requires a bit of common sense thinking, and no algorithm will help you with that.

OK: in order for you to get an equilateral triangle, you need to pick every other point on the circle. It doesn't really matter which point gets chosen first- what matters are the remaining two. So, after picking the first point, there are 2 points out of the remaining five which will work in the triangle, and after that 1 out of the remaining four. So, 2/5 * 1/4 =1/10.

Answer 3

There are 6C3 ways to pick 3 points. Of these 20 ways only 2 make equilateral triangles. So 2/20

Answer 4

So, what has to happen is that out of all six points A, B, C, D, E, and F, we have to choose either all of A, C, E or B, D, F,

It doesn't matter what order, so it's combinations.

6 choose 3 is 6!/3!*3! = 20 possible choices.

You can only win with two. 2/20 = 10% chance.

Answer 5

6C3 = 20 ways to choose the three points.

Due to symmetry,

Answer 6

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