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# How many different shortest routes can one use moving from

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How many different shortest routes can one use moving from [#permalink]  17 May 2005, 12:29
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How many different shortest routes can one use moving from town K to town M?
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Manager
Joined: 22 Apr 2005
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Rectangle 4x2
To get from one point to another staying on shortest route you can only down or to the right.
Each shortest route can be described as a sequence:
(x0, x1, x2, x3) where xi >=0 - number of steps down on vertical i.
x0 + x1 + x2 + x3 = 2
Number of solutions to this equation is our answer.
2C4 + 1C4 = 10
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amit_drummer wrote:
6!/(4!*2!)

Manager
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yup. Its 15.

there are two steps for down (d) and 4 steps right (r)

so it can be ddrrrr.

just need to find the permutation of this. which is 6!/(4!*2!) = 15
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emilem wrote:
amit_drummer wrote:
6!/(4!*2!)

emilem:

I like the solution posted by Shaq in testmagic forum. It works for this problem too.

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