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Math Help - Traingle from a set of points

  1. #1
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    Traingle from a set of points

    There are 10 points on a plane out of which 6 are collinear. How many triangles can be formed using these points as vertices.


    I have tried it in two methods, and i getting different answers, i am not sure what is wrong in my approach.

    first,

    10c3 - 6c3 = 100 i.e , taking three points from 10 and subtracting the chances in which all three points have been taken from the collinear points.

    second
    6c2 * 4c1 + 6c1*4c2 + 4c3 , i.e two from collinear and one from non-collinear + one from collinear and two from non-collinear + all three from non-collinear. I got 120.

    I think my first approach has some flaws, can anyone identify them.
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  2. #2
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    Both solutions are correct.
    BUT they both give 100, not 120.
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  3. #3
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    Thanks.

    But i am clueless what is wrong in my calculation to get 120 !

    20 *4 + 6 * 6 + 4 = 120.

    please if you can point out Which part of the second approach is wrong.
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  4. #4
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    Quote Originally Posted by kumaran5555 View Post
    Thanks.

    But i am clueless what is wrong in my calculation to get 120 !

    20 *4 + 6 * 6 + 4 = 120.

    please if you can point out Which part of the second approach is wrong.
    15 *4 + 6 * 6 + 4 = 100
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