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Pat will walk from intersection X to intersection Y along a

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Senior Manager
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Joined: 12 Mar 2006
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Schools: Kellogg School of Management
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Pat will walk from intersection X to intersection Y along a [#permalink] New post 13 Mar 2007, 22:30
Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?
(A) 6
(B) 8
(C) 10
(D) 14
(E) 16


Please explain the steps you used to arrive at the answer
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Director
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 [#permalink] New post 13 Mar 2007, 22:56
answer 10

My method is conventional, but I know it can be solved by conventional method as well.

Faster way is in 5 steps (u need to number every intersection)

Now through corner it may go through 2 ways, from first point horizontally it can go through 3 ways, from first point vertically it will will through 3 ways, from second point vertically it will go through 2 ways.

In toto it will go through 10 ways.

regards,

Amardeep
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 [#permalink] New post 13 Mar 2007, 23:35
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My way:

In any situation Pat would have to walk 3 streets up and 2 streets to the right, total 5 streets.

Use combinatorics:

5!/2!*3!=10
Director
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Joined: 13 Dec 2006
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 [#permalink] New post 13 Mar 2007, 23:50
Hey good one...
Its like number of ways of arranging 5 letters AAANN

regards,

Amardeep Sharma
  [#permalink] 13 Mar 2007, 23:50
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