Tricia drives 8 miles from home to work. If she must follow

Question

https://gmatclub.com/forum/download/file.php?id=24284 Tricia drives 8 miles from home to work. If she must follow the roads shown in the square grid below, and each square has a side of one mile, then how many routes can Tricia follow from home to work? A. 8 B. 12 C. 35 D. 45 E. 70 download.gif Home -------- | | | | | -------- | | | | | -------- | | | | | -------- | | | | | -------- Work

ywilfred · Accepted Answer

To get from home to work, she has to move up 4 times, and right 4 times.

So we can write a word UUUURRRR where U= up, R = right.

The number of ways to arrange this way is the number of routes she can take from home to work. So 8!/4!4! = 70

briks123 · Answer

This is actually a combinations question. She must walk up and to the right. There are four blocks up and four blocks to the right, so the answer is 8!/(4!4!)=70, E.

briks123 · Answer

So think about a person who has to walk this path:

Home 
------ 
| | | |
------
| | | |
------Work

(Home to work) The person has to walk three blocks to the right and two blocks down. So the shortest way includes walking five blocks. There are 5!=120 ways to walk five blocks but there are two restrictions. One is that she has to walk two blocks down and the other is that she has to walk three blocks to the right. So there are only 5!/(3!2!)=10 ways to walk home. Does that make sense?

nainaTan · Answer

I am not convinced with that response. The question asks how many different routes are available for Tricia. Every right and down in that case should be unique, right?

The way I see it, if every turn (right or down) is a step, Tricia needs to take a total of 8 such steps to reach her destination. So at every step, she has 2 choices, either right, or down (South and East if you must). As such, the number of possible routes should be 
2^8. Every route has to be unique. Can somebody please explain to me how my logic is incorrect?

Bunuel · Answer

Does she have 2 choices on EVERY step? For example, if she's on upper right corner, how many choices does she have?

AnanyaBakshi · Answer

she has to go NNNNEEEE

how many ways can we arrange these letters in different ways? 8! / (4! * 4!) = 70

iamyogi25 · Answer

From home to work, why are we restricting/assuming, it can only go in West and South direction. There could be a path where she goes south and then takes west and takes north etc. I understand the explanations given are assumed that the person can only move in west and south. What is going on? Any help is appreciated. Thanks.

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=24284

Tricia drives 8 miles from home to work. If she must follow the roads shown in the square grid below, and each square has a side of one mile, then how many routes can Tricia follow from home to work?

A. 8
B. 12
C. 35
D. 45
E. 70

The grid is 4 squares across and 4 squares down, so any  8 mile route  from home to work must be the shortest path: 4 moves east and 4 moves south.

Each route is just an ordering of those 8 moves, EEESSS, so the number of routes is 8!/(4!4!) = 70.

Answer: E.

We are not assuming she can only go east and south. The “8 miles” forces it. Any detour like going west, north, or extra loops would add miles and make the trip longer than 8. So only shortest paths count: exactly 4 east and 4 south moves.

iamyogi25 · Answer

Thank you, Bunuel. This makes sense.

Tricia drives 8 miles from home to work. If she must follow

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Tricia drives 8 miles from home to work. If she must follow

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