mathmath333
  • mathmath333
Find the number of triangles formed by the Red dots ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • mathmath333
1 Attachment
mathmath333
  • mathmath333
|dw:1442388135196:dw|
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{Find the number of triangles formed by the }\hspace{.33em}\\~\\ & \normalsize \color{red}{Red}\ \text{dots ? }\hspace{.33em}\\~\\ \end{align}}\)

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More answers

mathmath333
  • mathmath333
is this correct \(\Large {\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\ +\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\ +\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2} =243}\)
ganeshie8
  • ganeshie8
\(3+5+6 = 14\) number of triangles = \(\dbinom{14}{3} - \dbinom{3}{3} -\dbinom{5}{3}-\dbinom{6}{3}\)
Jhannybean
  • Jhannybean
I would like to see all the lines drawn out please? Thank you very much. :P (jk)
mathmath333
  • mathmath333
i didnt understand what u did
ganeshie8
  • ganeshie8
how many red dots are there ?
mathmath333
  • mathmath333
14
ganeshie8
  • ganeshie8
how many dots make one triangle ?
mathmath333
  • mathmath333
3
ganeshie8
  • ganeshie8
so, at first we might think that total possible triangles is \(\dbinom{14}{3}\)
ganeshie8
  • ganeshie8
but immediately we see that not all of them are proper triangles
mathmath333
  • mathmath333
ok i get it now
ganeshie8
  • ganeshie8
there will be some "red dot groups" that don't make a triangle what are they ?
mathmath333
  • mathmath333
colinear :D
Jhannybean
  • Jhannybean
Oh Im slowly seeing it now. Keep going!
ganeshie8
  • ganeshie8
BINGO! you got it!
mathmath333
  • mathmath333
yea the answer was 333
Jhannybean
  • Jhannybean
OH I GET IT NOW HAHA
ganeshie8
  • ganeshie8
maybe try explaining it to Jhanny and us so that you understand it more...
mathmath333
  • mathmath333
\({\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\ +\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\ +\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2} =243}\) what was the fault in this method
mathmath333
  • mathmath333
I hope jhannybean has no doubt ?
Jhannybean
  • Jhannybean
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.
ganeshie8
  • ganeshie8
Exactly! thats very well put!
mathmath333
  • mathmath333
yea she said "OH I GET IT NOW HAHA" she has not doubt .
Jhannybean
  • Jhannybean
Haha, Im a litle slow.
ganeshie8
  • ganeshie8
could you explain ur method
mathmath333
  • mathmath333
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
ganeshie8
  • ganeshie8
Looks you forgot to count the case : 1 red dot from each line
mathmath333
  • mathmath333
but i forgot the the case 1 dot from all 3 lines i got my mistake
ganeshie8
  • ganeshie8
good
mathmath333
  • mathmath333
thanks
mathmath333
  • mathmath333
|dw:1442389517882:dw|
imqwerty
  • imqwerty
kewl cx
mathmath333
  • mathmath333
profile pictures dont support gif images
imqwerty
  • imqwerty
yea :)
mathmath333
  • mathmath333
by the way what is 'kewl'
imqwerty
  • imqwerty
( ͡° ͜ʖ ͡°) *cool

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