Find the number of triangles formed by the Red dots ?

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Find the number of triangles formed by the Red dots ?

Mathematics
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\(\large \color{black}{\begin{align} & \normalsize \text{Find the number of triangles formed by the }\hspace{.33em}\\~\\ & \normalsize \color{red}{Red}\ \text{dots ? }\hspace{.33em}\\~\\ \end{align}}\)

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Other answers:

is this correct \(\Large {\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\ +\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\ +\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2} =243}\)
\(3+5+6 = 14\) number of triangles = \(\dbinom{14}{3} - \dbinom{3}{3} -\dbinom{5}{3}-\dbinom{6}{3}\)
I would like to see all the lines drawn out please? Thank you very much. :P (jk)
i didnt understand what u did
how many red dots are there ?
14
how many dots make one triangle ?
3
so, at first we might think that total possible triangles is \(\dbinom{14}{3}\)
but immediately we see that not all of them are proper triangles
ok i get it now
there will be some "red dot groups" that don't make a triangle what are they ?
colinear :D
Oh Im slowly seeing it now. Keep going!
BINGO! you got it!
yea the answer was 333
OH I GET IT NOW HAHA
maybe try explaining it to Jhanny and us so that you understand it more...
\({\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\ +\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\ +\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2} =243}\) what was the fault in this method
I hope jhannybean has no doubt ?
The 3, 5 , 6 correspond to the red dots per side, they = 14. But since each side with a specific amount of red dots that dont create a triangle, we subtract the possibilities of each side from the ones that do.
Exactly! thats very well put!
yea she said "OH I GET IT NOW HAHA" she has not doubt .
Haha, Im a litle slow.
could you explain ur method
to make triangle we need 1 red dot from one line and 2 red dots from other lines vice versa. count all 3 lines as such +vice versa
Looks you forgot to count the case : 1 red dot from each line
but i forgot the the case 1 dot from all 3 lines i got my mistake
good
thanks
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kewl cx
profile pictures dont support gif images
yea :)
by the way what is 'kewl'
( ͡° ͜ʖ ͡°) *cool

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