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Math Help - Repetition with Permutations-Number of Routes on a Grid Help?

  1. #1
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    Repetition with Permutations-Number of Routes on a Grid Help?

    How many routes are possible from A to B in this diagram:

    Untitled photo by MightyOwned | Photobucket

    I know it's a crap paint diagram. But you get the idea.

    The answer is apparently 600. I tried doing 5!/(3!2!) X 6!/(3!3!) + 5!/(3!2!) X 6!/(4!2!) but no luck.

    Please help.
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  2. #2
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    Re: Repetition with Permutations-Number of Routes on a Grid Help?

    Quote Originally Posted by MOMighty View Post
    How many routes are possible from A to B in this diagram:
    Untitled photo by MightyOwned | Photobucket
    I know it's a crap paint diagram. But you get the idea.The answer is apparently 600. I tried doing 5!/(3!2!) X 6!/(3!3!) + 5!/(3!2!) X 6!/(4!2!) but no luck.Please help.
    WHY do you use all those special formats?
    It makes it so hard to read.
    And you are correct, that is a truly poor diagram.

    Note that the two grids share two lattice points.
    We need to count the paths through those two points: inclusion/exclusion.

    2\left( {\frac{{5!}}{{3! \cdot 2!}}} \right)\left( {\frac{{6!}}{{3! \cdot 3!}}} \right) - \left( {\frac{{5!}}{{3! \cdot 2!}}} \right)^2
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