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Premutations and combinations 2

  1. Dec 12, 2005 #1
    Four lattices are selected from 5*4 grid board indicated in the figure above so that they form the corners of a rectangle having sides parallel to the edges of the board. How many different rectangles can be formed in this way?
    Can anyone give me some clues to answer this question?
    Thanks:approve:
     

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  3. Dec 12, 2005 #2

    siddharth

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    You need to choose 4 lines from you lattice to make the rectangle. These 4 lines will decide what the 4 sides in your rectangle are.

    What are the valid ways in which you can choose them?

    Let's say there are 6 horizontal(H) and 5 vertical lines(V) in the grid.
    Can you choose all four lines from only the horizontal set of lines? Similarly, can you choose all four lines from only the vertical set of lines?
    How about 3H - 1V or 2H - 2V?
     
    Last edited: Dec 12, 2005
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