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# Pat will walk from intersection X to intersection Y along a

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Senior Manager
Joined: 12 Mar 2006
Posts: 367
Schools: Kellogg School of Management
Followers: 2

Kudos [?]: 36 [0], given: 3

Pat will walk from intersection X to intersection Y along a [#permalink]  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

Attachments

fig1.doc [23 KiB]

Director
Joined: 13 Dec 2006
Posts: 521
Location: Indonesia
Followers: 6

Kudos [?]: 104 [0], given: 0

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
Director
Joined: 05 Feb 2006
Posts: 902
Followers: 1

Kudos [?]: 50 [1] , given: 0

1
KUDOS
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
Joined: 13 Dec 2006
Posts: 521
Location: Indonesia
Followers: 6

Kudos [?]: 104 [0], given: 0

Hey good one...
Its like number of ways of arranging 5 letters AAANN

regards,

Amardeep Sharma
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