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A race car driver has to drive from the intersection A to in

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A race car driver has to drive from the intersection A to in  [#permalink]

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New post 03 Jun 2011, 09:23
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (01:39) correct 50% (02:06) wrong based on 28 sessions

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A race car driver has to drive from the intersection A to intersection B along the route that is confined to the square grid of four touchstones and three avenues shown in the map above. How many routes from A to B can the racer take that have minimum possible length?

A. 7
B. 9
C. 10
D. 14
E. 18


http://s3.amazonaws.com/production.grockit.com/content_images/production/1264222415/40_a.jpg

cant we solve this by combinatorics ? grockit gives solution via counting which is cumbersome.

Attachment:
40_a.jpg
40_a.jpg [ 9.39 KiB | Viewed 236 times ]

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Re: A race car driver has to drive from the intersection A to in  [#permalink]

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New post 03 Jun 2011, 09:37
bblast wrote:
A race car driver has to drive from the intersection A to intersection B along the route that is confined to the square grid of four touchstones and three avenues shown in the map above. How many routes from A to B can the racer take that have minimum possible length?

7
9
10
14
18

http://s3.amazonaws.com/production.grockit.com/content_images/production/1264222415/40_a.jpg

cant we solve this by combinatorics ? grockit gives solution via counting which is cumbersome.


Count the number of columns, say c
Count the number of rows, say r

\(Ways = C^{(c+r)}_{c}\)
OR
\(Ways = C^{(c+r)}_{r}\)

In this figure,
c=2
r=3
c+r=5
\(Ways = C^{5}_{3} = 10\)

Ans: "C"
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Re: A race car driver has to drive from the intersection A to in  [#permalink]

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New post 03 Jun 2011, 09:51
1
UUULL (shortest possible way includes 3 UPs and 2 Lefts)
No. of arrangement includes = 5! / (3! * 2!) = 10
C is the quick answer.
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Re: A race car driver has to drive from the intersection A to in  [#permalink]

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New post 11 Apr 2019, 10:59
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Re: A race car driver has to drive from the intersection A to in   [#permalink] 11 Apr 2019, 10:59
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