BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

In how many ways can the letters of word "EDUCATION&quo

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

by EconomistGMATTutor » Sat Feb 17, 2018 8:42 am
VJesus12 wrote:In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels, as well as all the Consonants, always appear together?

A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!

The OA is D.

Why is D? I'm confused here. Experts, may you give me some help? Please.
Hello Vjesus12.

Let's take a look at the question.

EDUCATION has 5 vowels and 4 consonants. Hence, there are 5! ways of arranged the vowels and there are 4! ways to arrange the consonants.

Now, let's call A to all the vowels and B all the consonants together. Hence, we have two ways to arrange them, that is to say, AB and BA.

Finally, the total ways of arrange the vowels and consonants as asked are 5!*4!*2 = 5!*4!*2!.

Therefore, the correct answer is the option D.

I hope this answer may help you.

Feel free to ask me again if you have a doubt.

Regards.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sat Feb 17, 2018 10:12 am
VJesus12 wrote:In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels, as well as all the Consonants, always appear together?

A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!
VOWELS: E, U, A, I, O
CONSONANTS: D, C, T, N

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

Stage 1: Arrange the 5 vowels
We can arrange n unique objects in n! ways
So, we can arrange the 5 vowels in 5! ways
In other words, we can complete stage 1 in 5! ways

Stage 2: Arrange the 4 consonants
There are 4 unique objects to arrange.
We can complete stage 2 in 4! ways

Stage 3: The two groups of letters (the vowel group and the consonant group)
There are two options:
1) CONSONANTS-VOWELS
1) VOWELS-CONSONANTS
We can complete stage 3 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete the 3 stages (and thus arrange all 9 letters) in (5!)(4!)(2) ways.

Answer: D
--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Feb 18, 2018 3:18 am
VJesus12 wrote:In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels, as well as all the Consonants, always appear together?

A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!.
Number of ways to arrange the 5 vowels E, A, U, I, and O = 5!.
Number of ways to arrange the 4 consonants D, C, T and N = 4!.
To combine the options above, we multiply:
5!4!.
Since VOWELS-CONSONANTS and CONSONANTS-VOWELS both constitute viable arrangements, the result above must be multiplied by 2:
5!4!2.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Thu Feb 22, 2018 4:58 pm
VJesus12 wrote:In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels, as well as all the Consonants, always appear together?

A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!
We need to determine the number of ways to arrange the letters of word "EDUCATION" such that all the vowels as well as all the consonants always appear together. We start by arranging the given word with vowels together with the consonants together.

[EUAIO] [DCTN]

We first see that there are 2 ways to arrange [EUAIO] and [DCTN]: [EUAIO] [DCTN] and [DCTN] [EUAIO].

Next we must determine the number of arrangements for the letters in [EUAIO] and in [DCTN].

[EUAIO] can be arranged in 5! ways.

[DCTN] can be arranged in 4! ways.

Thus, the total number of ways to arrange the letters of word "EDUCATION" such that all the vowels as well as all the consonants always appear together is 5! x 4! x 2, or 5! x 4! x 2!.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1