How many ways can we arrange the word PARALLEL that the vowels are

Question

How many ways can we arrange the word PARALLEL that the vowels are kept together?

A) 120
B) 144
C) 288
D) 360
E) 600

hudacse6 · Answer

PARALLEL
So, {AAE}, {P},{R},{L},{L},{L}= 6! / 3! = 120 ( Divide by 3! coz we have 3L)
 and, AAE = 3!/2! = 3 
Therefore, 120*3=360
Answer = D.
 Am I correct?

saniabassi · Answer

First seperate all vowels from the word and write them seperately and count the vowels as one letter
P R L L L {A A E}= 6! 
and then write the no. of vowels (3!) and divide them by the repeated letters
  =360

BrentGMATPrepNow · Answer

Take the task of arranging the letters and break it into   stages  .

Stage 1 : "glue" the three vowels (A, A and E) together. 
There are three possible outcomes: AAE, AEA and EAA 
So, we can complete stage 1 in  3  ways 
This ensures that the three vowels are kept together.

NOTE: We now have the following 6 objects to arrange: P, R, L, L, L and the glued-together-vowels

Stage 2 : Arrange the following 6 objects: P, R, L, L, L and the glued-together-vowels
Notice that 3 of our objects are  identical  L's

----ASIDE------------------
When we want to arrange a group of items in which some of the items are  identical , we can use something called the MISSISSIPPI rule. 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 !)]
-----------------------

In P, R, L, L, L and the glued-together-vowels: 
There are  6  objects in total 
There are  3  identical L's

So the total number of possible arrangements =  6 !/( 3 !) = 120
So, we can complete stage 2 in  120  ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus arrange the letters) in  (3)(120)  ways (= 360 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS 
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fireagablast · Answer

P
AA
R
LLL
E

(AE)PRLLL = 6!/3! --> for base arrangements glue A and E; remember to divide by L repeats
AAE = 3!/2! = for the arrangements of glued A and E; remember to divide by A repeats

3!/2!*6!/3! = 3*120 = 360

ZulfiquarA · Answer

PARALLEL
Elements that are meant to be together: 3 (AAE) Other elements: 5 (PRLLL)
Arrangements: 
AAE=3*2*1/2! (Division by 2! because there are two A) = 3
PRLLL=5*4*3*2*1/3! (Division by 3! because there are three L) =20
3*20=60
Note that the combination AAE can be placed in 6 different way in the whole word: 60*6=360  (D)

bumpbot · Answer

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How many ways can we arrange the word PARALLEL that the vowels are

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How many ways can we arrange the word PARALLEL that the vowels are

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