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Math Help - Number of routes

  1. #1
    MHF Contributor chiph588@'s Avatar
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    Number of routes

    How many routes are there from the lower left corner to the upper right corner of an m*n grid if we are restricted to traveling only to the right or up? For example, in a 1*1 grid,
    only two routes exist : right,up or up,right.
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    Quote Originally Posted by chiph588@ View Post
    How many routes are there from the lower left corner to the upper right corner of an m*n grid if we are restricted to traveling only to the right or up? For example, in a 1*1 grid,
    only two routes exist : right,up or up,right.
    Let U stand for moving up one grid mark and R is right one.
    Now to make the trip we must use m R's and n U's.
    \underbrace {RRR \cdots RR}_m\underbrace {UUU \cdots UU}_n, how many ways can we rearrange that string?
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by Plato View Post
    Let U stand for moving up one grid mark and R is right one.
    Now to make the trip we must use m R's and n U's.
    \underbrace {RRR \cdots RR}_m\underbrace {UUU \cdots UU}_n, how many ways can we rearrange that string?
    would it be  mn+1?
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    Quote Originally Posted by chiph588@ View Post
    would it be  mn+1?
    NO indeed!
    It is an arrangement with repetitions.
    \frac{{\left( {m + n} \right)!}}<br />
{{\left( {m!} \right)\left( {n!} \right)}}<br />
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