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mathmath333

  • one year ago

Counting Problem

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{There are \(10\) points in a plane of which \(4\) are collinear. }\hspace{.33em}\\~\\ & \normalsize \text{No other \(3\) points are collinear.}\hspace{.33em}\\~\\ & \normalsize \text{Find the number of lines that can be drawn .}\hspace{.33em}\\~\\ \end{align}}\)

  2. ganeshie8
    • one year ago
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    is the answer \(\dbinom{6}{2} + 6*4\) ?

  3. mathmath333
    • one year ago
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    10C2-4C2+1

  4. ganeshie8
    • one year ago
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    right, both are same just a +1 is missing in my earlier reply

  5. mathmath333
    • one year ago
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    how u got that

  6. ganeshie8
    • one year ago
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    forget about 4 collinear points

  7. ganeshie8
    • one year ago
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    then you have 6 points, you know that any two points determine a line so how many lines can you make using 6 points ?

  8. mathmath333
    • one year ago
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    6c2

  9. ganeshie8
    • one year ago
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    next, from each of these 6 points, you can draw a line to each of the 4 collinear points, yes ?

  10. mathmath333
    • one year ago
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    yes

  11. ganeshie8
    • one year ago
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    |dw:1440183836929:dw|

  12. ganeshie8
    • one year ago
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    how many lines can you draw from those 6 points to those 4 collinear points ?

  13. mathmath333
    • one year ago
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    6C4

  14. ganeshie8
    • one year ago
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    |dw:1440183971999:dw|

  15. ganeshie8
    • one year ago
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    nope, notice that from each of those 6 points, you can draw exactly 4 lines to those collinear points

  16. mathmath333
    • one year ago
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    4*6

  17. ganeshie8
    • one year ago
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    Yes, so far the count is \(\dbinom{6}{2}+4*6\) can you guess the one line that is missing ?

  18. mathmath333
    • one year ago
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    |dw:1440184361598:dw|

  19. ganeshie8
    • one year ago
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    Thats it!

  20. ganeshie8
    • one year ago
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    so the final answer is \(\dbinom{6}{2} + 6*4+1\)

  21. mathmath333
    • one year ago
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    ok thnsk

  22. ganeshie8
    • one year ago
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    your textbook answer counts it in a different way

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