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October 26th, 2009, 09:25 AM  #1 
Newbie Joined: Oct 2009 Posts: 3 Thanks: 0  Number of possible outcomes when driving
I'm going to try and explain this question as well as I can  1. You live in a city. 2. The city is 10 (city) blocks wide and 10 blocks high (like a perfect grid) 3. Your house is on the left corner of the bottommost left block, or the most southwestern house in the city. 4. Your friend's house in on the right corner of the top right block, of the most northeastern house in the city. How many possible routes are there to get from your house to your friend's house? I would have no idea where to start in figuring this out? 
October 26th, 2009, 10:31 AM  #2 
Senior Member Joined: Oct 2009 Posts: 105 Thanks: 0  Re: Number of possible outcomes when driving
It depends, are we allowed to cross over a point in one of our earlier paths? Also, are we going from block to block, or are we just staying on the outer lines going from corner to corner?

October 26th, 2009, 01:06 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,274 Thanks: 1959 
If the journey is limited to the length of 10 blocks (going east) and ten blocks (going north), there are C(20,10) routes.

October 27th, 2009, 07:51 AM  #4 
Newbie Joined: Oct 2009 Posts: 3 Thanks: 0  Re: Number of possible outcomes when driving
Sorry Six, I forgot to mention, only north and west. Skipjack, thanks so much for the answer. I suppose if you were free to go back south or east the options become infinite, huh? 
October 27th, 2009, 07:53 AM  #5 
Newbie Joined: Oct 2009 Posts: 3 Thanks: 0  Re: Number of possible outcomes when driving
I realize I don't know what this means: C(20,10) 
October 27th, 2009, 08:19 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,274 Thanks: 1959 
It's one of various notations used for a binomial coefficient. The route is a total of 20 blocks, of which any 10 are north.

October 27th, 2009, 02:08 PM  #7  
Senior Member Joined: Oct 2009 Posts: 105 Thanks: 0  Re: Number of possible outcomes when driving Quote:
As long as I am not allowed to cross a path I went on earlier, it is still finite.  

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