Hello,

I drew two graphs in the picture below. the first one has a triangle whose tip on top and the second triangle whose tip on the bottom. I want to make sure if the two cases are repetitive or they could be counted separately. The correct answer is 18. However, If there were another option which is 36, I would have been stuck between 18 and 36. Thank you.

I think they are separate - youâ€™re not choosing the same points after all.

Can you elaborate on that a little bit more? Thank you.

In the example you showed above, they are from different points, so are different cases.

But the correct answer is 18 not 36.

I think youâ€™re focusing on the wrong part. If we look at Gregâ€™s solution, what did he do?

- He considered two cases: two points on bottom and one point on top, and one point on bottom and two points on top.
- He found the number of ways for one case (which is 9)
- He then multiplied by 2 to consider the other case as well.

Notice that at no point did we have to take the two triangles you created in the original problem as same - and they indeed arenâ€™t. In fact, the first triangle you drew is part of the first group (of which there are 9 triangles), and the second triangle is part of the second group (of which there are 9 triangles). So itâ€™s a case of 9 + 9, not 18 + 18.

Does that help?

Hello. Thanks a lot for your help. Iâ€™m confused about how you got 9.

I recommend rewatching Gregâ€™s solution (you can see the recording on gregmat.com/feed) - he explains where the 9 comes from.

The link doesnâ€™t work.

Is this the right class?

Yes. Thank you.