Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location...

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Tue May 05, 2020 1:20 pm

Veritas Prep

Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location. If Pavel travels only along streets and does not travel diagonally, the shortest possible route connecting the two points is exactly 14 blocks. How many different 14-block routes may Pavel take to travel the shortest possible distance to his aunt’s house?

A. 14
B. (14!)/(8!6!)
C. (22!)/(14!8!)
D. 8!6!
E. 14!8!6!

The OA is B

Given the information, we deduce that Pavel can travel the 14-block distance in many possible ways. To understand this, draw an 8*6 rectangle, with 8 equally spaced horizontal lines, with each depicting eastern direction and the gap between them, depicting 1-black distance.

Similarly, draw 6 vertical lines, as shown in the attached image.

Say each eastern side 1-block distance = E and each northern side distance = N; thus, Pavel has to travel 6 Es and 8 Ns. However, these Es and Ns can be in any combination. For example, in the image, Pavel travels NENENENENNEENNEE.

So, there are 8 + 6 = 14 blocks

No. of ways to choose them = 14!; however, since 8 Ns and 6Es are identical, we must divide 14! by 8! and 6!.

So, the required no. of ways = 14!/(8!.6!)

The correct answer: B

Hope this helps!

-Jay
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