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Math Help - parallel lines

  1. #1
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    parallel lines

    If a set of 10 parallel lines are intersected by a set of 13 other parallel lines,then find the number of parallelograms formed?

    I m not able to undertsand the question ..is there a standard formula for this type of questions
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let S_1, \ S_2 be the two sets of parallel lines. A paralleogram is formed by a pair of lines from S_1 and a pair of lines from S_2. So, the number of parallelograms depends on how many pairs can take from S_1 and S_2.

    This number is C_{10}^2\cdot C_{13}^2=45\cdot 78=3510

    Generally, if there is a set of n parallel lines and another set of m parallel lines, the number of parallelograms is C_n^2\cdot C_m^2
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  3. #3
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    will this formula hold good if both m and n are equal like in a chess board 9 parallel lines intersecting 9 parallel lines so if i apply ur formula 9C2*9C2 is not equal to 64 .


    so i did like this number of lines -1C (min number of lines -1)
    so 22-1C10-1=21C9
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  4. #4
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    Quote Originally Posted by arunachalam.s View Post
    will this formula hold good if both m and n are equal like in a chess board 9 parallel lines intersecting 9 parallel lines so if i apply ur formula 9C2*9C2 is not equal to 64 .
    You have a missunderstaning about the count.
    Look at the attached 3x3 grid.
    There are a total of nine rectangles in that grid: \binom{3}{2}\binom{3}{2}=9.
    Attached Thumbnails Attached Thumbnails parallel lines-gr33.gif  
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  5. #5
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    k i understand thank u
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