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October 26th, 2009, 08:25 AM   #1
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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 bottom-most left block, or the most south-western house in the city.
4. Your friend's house in on the right corner of the top right block, of the most north-eastern 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?
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October 26th, 2009, 09:31 AM   #2
six
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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?
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October 26th, 2009, 12:06 PM   #3
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If the journey is limited to the length of 10 blocks (going east) and ten blocks (going north), there are C(20,10) routes.
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October 27th, 2009, 06:51 AM   #4
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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?
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October 27th, 2009, 06:53 AM   #5
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Re: Number of possible outcomes when driving

I realize I don't know what this means:

C(20,10)
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October 27th, 2009, 07:19 AM   #6
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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.
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October 27th, 2009, 01:08 PM   #7
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Re: Number of possible outcomes when driving

Quote:
Originally Posted by groundwar
I suppose if you were free to go back south or east the options become infinite, huh?
Not necessarily...

As long as I am not allowed to cross a path I went on earlier, it is still finite.
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