In how many ways can a 4-letter word be formed from the

Expert replies

Previous Topic Next Topic

swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

In how many ways can a 4-letter word be formed from the

by swerve » Thu Jan 31, 2019 9:39 am

Timer

00:00

Your Answer

Global Stats

In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.

A. 36
B. 144
C. 288
D. 864
E. 1728

The OA is D

Source: e-GMAT

Source: Beat The GMAT — Problem Solving | Thu Jan 31, 2019 9:39 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Jan 31, 2019 10:09 am

swerve wrote:In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.

A. 36
B. 144
C. 288
D. 864
E. 1728
Source: e-GMAT

$$?\,\,:\,\,\# \,\,4\,\,{\rm{distinct}}\,\,{\rm{letters}}\,\,\,\left\{ \matrix{
\,2\,\,{\rm{vowels}} \hfill \cr
\,2\,\,{\rm{consonants}} \hfill \cr} \right.$$
$$?\,\,\, = \,\,\,\underbrace {C\left( {4,2} \right)}_{{\rm{for}}\,\,{\rm{vowels}}} \cdot \underbrace {C\left( {4,2} \right)}_{{\rm{for}}\,\,{\rm{consonants}}} \cdot \underbrace {\,\,{P_4}\,\,}_{{\rm{chosen}}\,4\,,\,\,{\rm{permutations}}}\,\,\, = \,\,\,{{4 \cdot 3} \over 2} \cdot {{4 \cdot 3} \over 2} \cdot 4!\,\,\, = \,\,\,6 \cdot 6 \cdot 24\,\,\, = \,\,\,864$$

The correct answer is therefore (D).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8132; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Feb 04, 2019 5:23 pm

swerve wrote:In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.

A. 36
B. 144
C. 288
D. 864
E. 1728

There are 4C2 = 6 ways to choose 2 vowels from 4 vowels, and similarly, there are 4C2 = 6 ways to choose 2 consonants from 4 consonants Therefore, there are 6 x 6 = 36 different words with a particular set of 2 vowels and 2 consonants.

However, for each of these 36 words, since the 4 letters can be arranged in any order, there are a total of 4! x 36 = 24 x 36 = 864 6 words possible.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

In how many ways can a 4-letter word be formed from the

by regor60 » Tue Feb 05, 2019 7:21 am

swerve wrote:In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.

A. 36
B. 144
C. 288
D. 864
E. 1728

The OA is D

Source: e-GMAT

BIDE....BODE...etc $$$$

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Feb 05, 2019 10:22 am

Hi regor60,

I agree that this prompt is poorly-worded. The "intent" is to ask for every 4-letter arrangement that fits the given restrictions, INCLUDING "words" that do not appear in the dictionary (re: arrangements that are not actually words). GMAT question-writers are far more specific with how they word their questions, so you won't face this type of ambiguity on Test Day.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue Feb 05, 2019 10:57 am

[email protected] wrote:Hi regor60,

I agree that this prompt is poorly-worded. The "intent" is to ask for every 4-letter arrangement that fits the given restrictions, INCLUDING "words" that do not appear in the dictionary (re: arrangements that are not actually words). GMAT question-writers are far more specific with how they word their questions, so you won't face this type of ambiguity on Test Day.

GMAT assassins aren't born, they're made,
Rich

Gotcha.

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

vowels and consonants

by GMATGuruNY » Tue Feb 05, 2019 12:09 pm

swerve wrote:In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.

A. 36
B. 144
C. 288
D. 864
E. 1728

Alternate approach:

Case 1: VVCC, where the first two letters are vowels and the last 2 letters are consonants
Number of options for the first vowel = 4. (Any of the 4 vowels)
Number of options for the second vowel = 3. (Any of the 3 remaining vowels)
Number of options for the first consonant = 4. (Any of the 4 consonants)
Number of options for the second consonant = 3. (Any of the 3 remaining consonants)
To combine these options, we multiply:
4*3*4*3 = 144.

Other cases:
To account for every possible position for the two selected vowels and the two selected consonants, we must multiply the result above by the number of ways to arrange VVCC.
The number of ways to arrange 4 distinct letters = 4!.
But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be arranged.
The reason:
When identical elements swap positions, the arrangement does not change.
Here, we must divide by 2! to account for VV and by another 2! to account for CC:
4!/(2!2!) = 6.

Thus:
Total number of possible words = 144 * 6 = 864.

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

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review