It is currently 18 Oct 2017, 22:53

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many 5 letter combinations can be made from the letters

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 444

Kudos [?]: 1789 [1], given: 289

How many 5 letter combinations can be made from the letters [#permalink]

Show Tags

New post 18 Jul 2014, 11:53
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:20) correct 31% (01:43) wrong based on 204 sessions

HideShow timer Statistics

How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?

A. 21
B. 42
C. 120
D. 600
E. 720
[Reveal] Spoiler: OA

Kudos [?]: 1789 [1], given: 289

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128792 [0], given: 12183

Re: How many 5 letter combinations can be made from the letters [#permalink]

Show Tags

New post 18 Jul 2014, 11:58
Expert's post
6
This post was
BOOKMARKED
goodyear2013 wrote:
How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?

A. 21
B. 42
C. 120
D. 600
E. 720


{vowel}{X}{X}{X}{consonant}

VERMONT consists of 2 vowels and 5 consonants:

The number of way to choose a vowel for the first letter = \(C^1_2=2\).
The number of way to choose a consonant for the last letter= \(C^1_5=5\).

The number of ways to choose middle three letters out of 5 remaining letters = \(C^3_5=10\).
The number of arrangements of these three letters = 3! = 6.

Total = 2*5*10*6 = 600.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128792 [0], given: 12183

1 KUDOS received
Current Student
avatar
Joined: 25 Jun 2014
Posts: 42

Kudos [?]: 58 [1], given: 22

GMAT 1: 690 Q48 V37
WE: Operations (Computer Software)
Re: How many 5 letter combinations can be made from the letters [#permalink]

Show Tags

New post 25 Feb 2016, 02:04
1
This post received
KUDOS
Vowel: E O

Consonants: V R M N T

First letter can be filled in 2 Ways ( As the question states that "first letter has to be a vowel")
Fifth letter can be filled in 5 Ways ( As the question states that "the last letter has to be a consonant")

Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter

Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways

So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 5 ways = 600

Answer D
_________________

Did I Help You..If Yes.. Then Kudos Please.. :-)

Kudos [?]: 58 [1], given: 22

Intern
Intern
avatar
Joined: 25 Feb 2016
Posts: 2

Kudos [?]: 2 [0], given: 0

Re: How many 5 letter combinations can be made from the letters [#permalink]

Show Tags

New post 25 Feb 2016, 04:06
i normally tend to do it using fill in the blanks

- - - - - the first place has condition which can be either O or E and the last place by V.R.M,N,T as for the 2nd 3rd and 4th we have the remaning ones

so its like first place =2
Last place 5
second place 5
third place 4 and 4th place 3

so number of combinations = 2*5*4*3*5 = 600

so 600 ways

Kudos [?]: 2 [0], given: 0

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16681

Kudos [?]: 273 [0], given: 0

Premium Member
Re: How many 5 letter combinations can be made from the letters [#permalink]

Show Tags

New post 26 Jun 2017, 13:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Manager
Manager
avatar
B
Joined: 18 Jun 2017
Posts: 60

Kudos [?]: 2 [0], given: 166

Re: How many 5 letter combinations can be made from the letters [#permalink]

Show Tags

New post 04 Aug 2017, 05:20
VERMONT has 2 vowels and 5 consonants.
Hence first letter can be chosen in 2 ways.
Hence last letter can be chosen in 5 ways.
Remaining 3 can be selected in 5*4*3 ways.
So total ways the letters can be arranged in that sequence
2*5*4*3*5=600 ways.
Option D.

Kudos [?]: 2 [0], given: 166

Re: How many 5 letter combinations can be made from the letters   [#permalink] 04 Aug 2017, 05:20
Display posts from previous: Sort by

How many 5 letter combinations can be made from the letters

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.