## Lachlan1996 2 years ago Help with mathematical combinations please. Points A, B, C, D, E, F, G, H, and I are arranged in two rows such that we have A - B - C - D - E and F - G - H - I How many triangles can be formed having vertices chosen from these points? How many of these triangles have the point A as one of their vertices?

1. Lachlan1996

Sorry it is A - B - C - D - E F - G - H - I

2. Lachlan1996

Awesome thank you for visiting unklerhaukus!!!

3. UnkleRhaukus

|dw:1360476356312:dw|

4. Lachlan1996

Yes they are to act as the vertices of triangles.

5. UnkleRhaukus

so either two points are from the top line (and one from the bottom line) or one point is from the top line (and two from the bottem line)

6. Lachlan1996

Hmm i see, let me try that, i wasnt sure how to interpret it.

7. UnkleRhaukus

because if all three points were on the same line , you couldn't make a triangle

8. Lachlan1996

Yes that appears to work, 5C1 x 4C2 and 5C2 x 4C1 which adds to 70

9. Lachlan1996

Though can I ask how you determine how to do these questions? I havent really got a problem solving type of mind, so i find it difficult to think laterally.

10. UnkleRhaukus

$^nC_k = \frac{n!}{k!(n-k)!}$

11. Lachlan1996

No i understand the general formula of the combination theory. I just often have difficulty understanding how I am meant to approach the question, what guidelines I need to follow.

12. Lachlan1996

Once you had explained those guidelines i knew exactly what to do, i just dont know how to determine the parameters to follow.

13. UnkleRhaukus

i like to start with a picture usually

14. Lachlan1996

Are there any other tricks you can use to figure out whats going on? or is it just trying to pull apart the question, and making assumptions to rules.

15. UnkleRhaukus

im not sure how to answer that,

16. Lachlan1996

Ah well, im sure i'll just have to pick it up as I go. You've helped enough already. Thank you very much for the assistance. I wish you a good afternoon. Thank you for the help mate, I appreciate the effort :) Have a good one mate, and stay well!

17. UnkleRhaukus

sometimes rewriting the question into a simpler form can help