Question

Find the number of triangles formed by the Red dots ?

Answer 1

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

Answer 2

is this correct


\(\Large {\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\
+\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\
+\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2}
=243}\)

Answer 3

\(3+5+6 = 14\)

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

Answer 4

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

Answer 5

i didnt understand what u did

Answer 6

how many red dots are there ?

Answer 7

14

Answer 8

how many dots make one triangle ?

Answer 9

3

Answer 10

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

Answer 11

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

Answer 12

ok i get it now

Answer 13

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

Answer 14

colinear :D

Answer 15

Oh Im slowly seeing it now. Keep going!

Answer 16

BINGO! you got it!

Answer 17

yea the answer was 333

Answer 18

OH I GET IT NOW HAHA

Answer 19

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

Answer 20

\({\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\
+\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\
+\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2}
=243}\)

what was the fault in this method

Answer 21

I hope jhannybean has no doubt ?

Answer 22

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.

Answer 23

Exactly! thats very well put!

Answer 24

yea she said

"OH I GET IT NOW HAHA"

she has not doubt .

Answer 25

Haha, Im a litle slow.

Answer 26

could you explain ur method

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

good

Answer 31

thanks

Answer 32

kewl cx

Answer 33

profile pictures dont support gif images

Answer 34

yea :)

Answer 35

by the way what is 'kewl'

Answer 36

( ͡° ͜ʖ ͡°) *cool