Find the number of triangles formed by the Red dots ?

- mathmath333

Find the number of triangles formed by the Red dots ?

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- mathmath333

##### 1 Attachment

- mathmath333

|dw:1442388135196:dw|

- 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

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

\(3+5+6 = 14\)
number of triangles = \(\dbinom{14}{3} - \dbinom{3}{3} -\dbinom{5}{3}-\dbinom{6}{3}\)

- Jhannybean

I would like to see all the lines drawn out please? Thank you very much. :P (jk)

- mathmath333

i didnt understand what u did

- ganeshie8

how many red dots are there ?

- mathmath333

14

- ganeshie8

how many dots make one triangle ?

- mathmath333

3

- ganeshie8

so, at first we might think that total possible triangles is \(\dbinom{14}{3}\)

- ganeshie8

but immediately we see that not all of them are proper triangles

- mathmath333

ok i get it now

- ganeshie8

there will be some "red dot groups" that don't make a triangle
what are they ?

- mathmath333

colinear :D

- Jhannybean

Oh Im slowly seeing it now. Keep going!

- ganeshie8

BINGO! you got it!

- mathmath333

yea the answer was 333

- Jhannybean

OH I GET IT NOW HAHA

- ganeshie8

maybe try explaining it to Jhanny and us so that you understand it more...

- 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

I hope jhannybean has no doubt ?

- 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

Exactly! thats very well put!

- mathmath333

yea she said
"OH I GET IT NOW HAHA"
she has not doubt .

- Jhannybean

Haha, Im a litle slow.

- ganeshie8

could you explain ur method

- 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

Looks you forgot to count the case : 1 red dot from each line

- mathmath333

but i forgot the the case 1 dot from all 3 lines i got my mistake

- ganeshie8

good

- mathmath333

thanks

- mathmath333

|dw:1442389517882:dw|

- imqwerty

kewl cx

- mathmath333

profile pictures dont support gif images

- imqwerty

yea :)

- mathmath333

by the way what is 'kewl'

- imqwerty

( ͡° ͜ʖ ͡°) *cool

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