Pavel has to visit his aunt, who lives exactly eight blocks north and

Question

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!

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

Bunuel · Accepted Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: B

It will probably come as a relief to learn that this very difficult problem boils down to simple combinatorics. If Pavel has to walk eight blocks north and six blocks east, we can express his route as NNNNNNNNEEEEEE. The question is thus a repeating elements permutation problem that asks us how many ways we can arrange those letters. (If this is confusing, start with smaller numbers. Say I have to walk two blocks north and one block east to get to the train station. I can walk NNE, NEN, or ENN, three different routes that will all get me to the train station.) This gives us (total # of letters)!/(# of N’s)!(# of E’s)!, or 14!/8!6!, answer (B).

chetan2u · Answer

ans B..
 for simplification, you can draw a box/rectangle with eight vertical and 6 horizontal lines...
 the Q asks u how can u travel from one vertex to opposite vertex along these lines..
And the shortest route will consist of 8 vertical and 6 horizontal moves..
so total ways are 14! out of which 8 are one kind and 6 of the other...
ways= 14!/(8!6!)

KarishmaB · Answer

This problem boils down to an arrangement problem. There are various ways in which you can cover 8 North blocks and 6 East blocks. Go North one block, then East one block, then North 2 blocks, then East 1 block, then North 2 blocks etc
You can represent the ways like this:
NENNENNEEEENNN
NNNNNNNNEEEEEE
NENENENENENENN
and so on...

The number of ways of arranging total 14 letters where 8 are of the same kind and another 6 of the same kind = 14!/(8!*6!)

hatemnag · Answer

Please Bunuel.
It is permutation not combination ?
I mean order matter or not ?

Bunuel · Answer

Yes, order matters. Pavel has to travel total of 14 blocks: 8 of them north and 6 east. So, he can go NNNNNNNNEEEEEE or EEEEEENNNNNNNN or NNNEEEEEENNNNN... Basically the number of possible routes is the number of permutations of 14 letters EEEEEENNNNNNNN, which is 14!/(8!6!). Similar questions to practice: in-a-city-where-all-streets-run-east-to-west-all-avenues-run-north-to-186781.html every-morning-casey-walks-from-her-house-to-the-bus-stop-104236.html josh-has-to-run-an-electrical-wire-from-point-a-to-point-b-99962.html as-per-the-given-figure-there-are-many-horizontal-and-134453.html pat-will-walk-from-intersection-a-to-intersection-b-along-a-68374.html as-per-the-given-figure-there-are-many-horizontal-and-134453.html alicia-lives-in-a-town-whose-streets-are-on-a-grid-system-126920.html in-city-a-the-streets-are-aligned-in-a-grid-where-the-east-136949.html the-diagram-above-shows-the-various-paths-along-which-a-mous-144271.html Hope it helps.

Kinshook · Answer

Given: 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. 
Asked: How many different 14-block routes may Pavel take to travel the shortest possible distance to his aunt’s house?

Let us consider the path followed by Pavel as a string consisting 8Ns & 6Es
For example NNNNNNNNEEEEEE

Number of ways of forming the string = 14!/8!6!

IMO B

ScottTargetTestPrep · Answer

Solution:
 
Let N be a “north” block (i.e., when Pavel travels north) and E be an “east” block (i.e., when he travels east). Thus, one path Pavel can go to his aunt’s house is NNNNNNNNEEEEEE and the total number of paths is 14! / (8!6!) (i.e., the number of ways one can arrange 8 N’s and 6 E’s in NNNNNNNNEEEEEE).

Answer: B

BrentGMATPrepNow · Answer

Here's one more approach.

As is already mentioned above, Pavel's route will consist of 14 steps (Norths and Easts). 
6 of those steps will be Easts and the rest will be Norths.

So, let's select the 6 steps that will be Easts and let the rest be Norths.

In how many ways can we select 6 of the 14 steps? 
Well, since the order  in which we select the steps  does not matter, we can use combinations. 
So, we can select the 6 steps in 14C6 ways. 
14C6 = 14!/(8!6!)

Answer: B

IMPORTANT: Notice that I said the order  in which we select the steps  does not matter. In other words, selecting steps 2, 4, 5, 8, 10, and 13 to be Easts is the same as selecting steps 4, 5, 10, 8, 13 and 2. Given this, we can use combinations.

Cheers,
Brent

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Pavel has to visit his aunt, who lives exactly eight blocks north and

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Pavel has to visit his aunt, who lives exactly eight blocks north and

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