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Pascals Triangle - Number of Routes on a Grid

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Deepa’s house is five blocks west and four blocks south of a bus stop. A store is three blocks west and one block south of the bus stop. How many ways can Deepa walk home if she wishes to stop on her way home by walking only west and south?

    2. Relevant equations



    3. The attempt at a solution

    (number of routes to the store) * (number of routes from store to home)

    = C (4,2) * C(5,2)

    = (4*3/2) * (5*4/2)

    = 6 * 10

    = 60 ways

    Therefore, Deepa can walk home in 60 ways if she wishes to stop by the store on her way home.

    Would anybody be able to confirm whether my answer is correct?

    Thanks
     
    Last edited: Dec 4, 2012
  2. jcsd
  3. Dec 4, 2012 #2

    haruspex

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    Not C(4,2). Try again.
     
  4. Dec 5, 2012 #3
    Must be C(4,1) then:

    C (4,1) * C(5,2)

    = (4) * (5*4/2)

    = 4 * 10

    = 40 ways

    Can anyone confirm this?

    Thanks!
     
  5. Dec 5, 2012 #4

    haruspex

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    40 looks right to me.
     
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