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mathmath333

  • one year ago

Find the number of triangles formed by the Red dots ?

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  1. mathmath333
    • one year ago
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  2. mathmath333
    • one year ago
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    |dw:1442388135196:dw|

  3. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{Find the number of triangles formed by the }\hspace{.33em}\\~\\ & \normalsize \color{red}{Red}\ \text{dots ? }\hspace{.33em}\\~\\ \end{align}}\)

  4. mathmath333
    • one year ago
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    is this correct \(\Large {\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\ +\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\ +\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2} =243}\)

  5. ganeshie8
    • one year ago
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    \(3+5+6 = 14\) number of triangles = \(\dbinom{14}{3} - \dbinom{3}{3} -\dbinom{5}{3}-\dbinom{6}{3}\)

  6. Jhannybean
    • one year ago
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    I would like to see all the lines drawn out please? Thank you very much. :P (jk)

  7. mathmath333
    • one year ago
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    i didnt understand what u did

  8. ganeshie8
    • one year ago
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    how many red dots are there ?

  9. mathmath333
    • one year ago
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    14

  10. ganeshie8
    • one year ago
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    how many dots make one triangle ?

  11. mathmath333
    • one year ago
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    3

  12. ganeshie8
    • one year ago
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    so, at first we might think that total possible triangles is \(\dbinom{14}{3}\)

  13. ganeshie8
    • one year ago
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    but immediately we see that not all of them are proper triangles

  14. mathmath333
    • one year ago
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    ok i get it now

  15. ganeshie8
    • one year ago
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    there will be some "red dot groups" that don't make a triangle what are they ?

  16. mathmath333
    • one year ago
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    colinear :D

  17. Jhannybean
    • one year ago
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    Oh Im slowly seeing it now. Keep going!

  18. ganeshie8
    • one year ago
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    BINGO! you got it!

  19. mathmath333
    • one year ago
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    yea the answer was 333

  20. Jhannybean
    • one year ago
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    OH I GET IT NOW HAHA

  21. ganeshie8
    • one year ago
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    maybe try explaining it to Jhanny and us so that you understand it more...

  22. mathmath333
    • one year ago
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    \({\dbinom{5}{1}*\dbinom{6}{2}+\dbinom{6}{1}*\dbinom{5}{2} \\ +\dbinom{3}{2}*\dbinom{6}{1}+\dbinom{6}{2}*\dbinom{3}{1} \\ +\dbinom{3}{1}*\dbinom{5}{2}+\dbinom{5}{1}*\dbinom{3}{2} =243}\) what was the fault in this method

  23. mathmath333
    • one year ago
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    I hope jhannybean has no doubt ?

  24. Jhannybean
    • one year ago
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    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.

  25. ganeshie8
    • one year ago
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    Exactly! thats very well put!

  26. mathmath333
    • one year ago
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    yea she said "OH I GET IT NOW HAHA" she has not doubt .

  27. Jhannybean
    • one year ago
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    Haha, Im a litle slow.

  28. ganeshie8
    • one year ago
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    could you explain ur method

  29. mathmath333
    • one year ago
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    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

  30. ganeshie8
    • one year ago
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    Looks you forgot to count the case : 1 red dot from each line

  31. mathmath333
    • one year ago
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    but i forgot the the case 1 dot from all 3 lines i got my mistake

  32. ganeshie8
    • one year ago
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    good

  33. mathmath333
    • one year ago
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    thanks

  34. mathmath333
    • one year ago
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    |dw:1442389517882:dw|

  35. imqwerty
    • one year ago
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    kewl cx

  36. mathmath333
    • one year ago
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    profile pictures dont support gif images

  37. imqwerty
    • one year ago
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    yea :)

  38. mathmath333
    • one year ago
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    by the way what is 'kewl'

  39. imqwerty
    • one year ago
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    ( ͡° ͜ʖ ͡°) *cool

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