Results 1 to 3 of 3

Math Help - Tree Diagrams/Grids - PLEASE HELP

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    11

    Exclamation Tree Diagrams/Grids - PLEASE HELP

    I'm having trouble with the following:

    You live at the south-west corner of a grid of streets 9 blocks north-to-south and 6 blocks east-to-west. How many possible efficient paths are there to your office at the north-east corner if the east-west block which begins at 3 blocks east and 4 blocks north of your home is closed?

    I'm stumped!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello bjanela
    Quote Originally Posted by bjanela View Post
    I'm having trouble with the following:

    You live at the south-west corner of a grid of streets 9 blocks north-to-south and 6 blocks east-to-west. How many possible efficient paths are there to your office at the north-east corner if the east-west block which begins at 3 blocks east and 4 blocks north of your home is closed?

    I'm stumped!!
    Suppose your home is H, your office O and that the block that's closed has A and B at its western and eastern ends, respectively.

    With no restrictions on the route, the number of routes from H to O is {^{15}C_6}=5005, since this is the number ways in which the positions of the 6 easterly 'legs' of the journey may be positioned within the 15 legs that make up the whole journey.

    The number of routes from H to A is similarly {^7C_3}=35 and the number of routes from B to O is {^7C_2}=21. Thus the number of routes from H to O via A and B is 35 \times 21 = 735. These represent the routes that are not available if AB is closed.

    So the number of available routes that don't go via A and B = 5005 - 735 = 4270.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    11

    Thumbs up

    What I did wrong was not include the combinations from B->O (7C2) That makes sense--thank you so much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability using tree diagrams
    Posted in the Statistics Forum
    Replies: 5
    Last Post: July 9th 2011, 04:24 PM
  2. multivariable tree diagrams
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 3rd 2011, 06:37 AM
  3. tree diagrams
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 21st 2010, 08:21 AM
  4. Alternative to tree diagrams?
    Posted in the Statistics Forum
    Replies: 3
    Last Post: July 24th 2009, 08:39 AM
  5. Using tree diagrams
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 23rd 2008, 03:35 AM

Search Tags


/mathhelpforum @mathhelpforum