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Math Help - inclusion and exclusion principle

  1. #1
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    tehran
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    inclusion and exclusion principle

    inclusion and exclusion principle-img2.jpg

    count the number of paths from A to B ? which you can just go right or up? (with inclusion and exclusion principle)

    * plz write the solution for a foolish person : )
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  2. #2
    MHF Contributor
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    Re: inclusion and exclusion principle

    Quote Originally Posted by mshou View Post
    count the number of paths from A to B ?
    This is not a question? It is a command? Therefore, no question mark is necessary?

    Let's introduce a coordinate system with origin at A and the unit length equal to the grid size. Then A has coordinates (0, 0) and B has coordinates (8, 7).

    There are two holes in the grid. A path goes through the first hole iff it goes through (3, 3). Let X be the set of such paths. A path goes through the second hole iff it goes through (5, 5) and (5, 6). Let Y be the set of such paths. You need to find |X ∪ Y| and subtract it from the number of paths from A to B in the grid without holes. By inclusion-exclusion principle, it is sufficient to find |X|, |Y| and |X ∩ Y|.
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