Josh has to run an electrical wire from point a to point b

Question

picture.jpg Josh has to run an electrical wire from point a to point b along a circuit that is restricted to the grid shown to the left. How many possible paths could Josh use that have the minimum possible length? A. 8 B. 10 C. 12 D. 15 E. 16

Bunuel · Accepted Answer

You can notice that in order the length to be minimum wire should only go UP and RIGHT: namely twice UP and 4 times RIGHT.

So combination of UURRRR: # of permutations of 6 letters out of which there are 2 identical U's and 4 identical R's is  \frac{6!}{2!4!}=15 .

Answer: D.

Hope it's clear.

BrentGMATPrepNow · Answer

This is a great candidate for applying the  Mississippi Rule 
The rule is useful for arranging a group of items in which some of the items are identical.
It goes like this:

If there are  n  objects where  A  of them are alike, another  B  of them are alike, another  C  of them are alike, and so on, then the total number of possible arrangements =  n !/ A !)( B !)( C !)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows: 
There are  11  letters in total 
There are  4  identical I's
There are  4  identical S's
There are  2  identical P's
So, the total number of possible arrangements =  11 !/ 4 !)( 4 !)( 2 !)]

-----NOW ONTO THE QUESTION--------
To get from point a to point b, we must travel UP (U) two times, and travel RIGHT (R) 4 times
In other words, we want to determine the number of DIFFERENT ways to arrange 2 U's and 4 R's 
let's apply the above rule.

There are  6  letters in total 
There are  2  identical U's
There are  4  identical R's
Total number of possible arrangements =  6 !/ 2 !)( 4 !)]
= 15

Answer:  D

RELATED VIDEO
 https://www.youtube.com/watch?v=aFFRoDM01RY

gurpreetsingh · Answer

Excellent approach.

Bunnel I was just wondering how much you got on Gmat? Have you given?

zisis · Answer

thanks! thats exactly what i was looking for ! If i recall correcty, you must be the GMATclub combinations expert

gurpreetsingh · Answer

He is expert in almost every topic of quant.

zisis · Answer

lol...then he will have lots of "stamps" :p

harshsingla · Answer

hi all 
please explain ..
if there is a rectangle and this rectangle is divided in to four equal rectangles by building roads inside it then how many ways are there with which one can reach from one corner to other diagonally opposite corner.
please try to explain in terms of combinations .like in terms of nCr etc.

thanks

gurpreetsingh · Answer

You need to find permutations of UURR = 4!/2!2! = 6

harshsingla · Answer

but how 4c2..???
please explain!!

shrouded1 · Answer

think of it like this
You have four moves to make to reach the opposite corner

two moves are up
and two moves are right

now, any order of moves would always get to the corner

the question really is that out of move1,2,3&4 which two you pick to be the Up move (the other two will be the right move). The ways to do this is C(4,2), choosing 2 out of 4.

email2vm · Answer

out of six we need to choose 4 on x-axis or out of six we need to choose 2 on y axis
so 6c2 or 6c4

QuantMadeEasy · Answer

n things can be arranged in n! ways
So, 6 things can be arranged in 6! ways

4 horizontal and 2 vertical paths can rearrange within themselves

So total number of ways = 6! / 4!x2! = 15
D is correct.

BrushMyQuant · Answer

Similar problem solved using 2 methods here

https://www.youtube.com/watch?v=YkdWxXZ05P4

Hope it helps!

bumpbot · Answer

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Josh has to run an electrical wire from point a to point b

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Josh has to run an electrical wire from point a to point b

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