Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 23 May 2015, 05:46

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The word NUGGET has six letters. What is the maximum # of

Author Message
TAGS:
Manager
Joined: 20 Oct 2003
Posts: 63
Location: Houston, TX
Followers: 1

Kudos [?]: 1 [0], given: 0

The word NUGGET has six letters. What is the maximum # of [#permalink]  24 May 2004, 08:10
The word NUGGET has six letters.

What is the maximum # of different arrangement of character strings (e.g. GETNGU) one can make, ensuring that the two G letters are at least one letter apart?
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 704 [0], given: 781

Re: Comb/Perm [#permalink]  24 May 2004, 09:14
jjomalls wrote:
The word NUGGET has six letters.

What is the maximum # of different arrangement of character strings (e.g. GETNGU) one can make, ensuring that the two G letters are at least one letter apart?

i might just screw this up..so study the solution and let me know.

1. find out number of arrangements of NUGGET ( no restrictions)

6!/2! is the total number of ways ( remember the signals problem, we have to divide by 2! to take care of the repitition of G)

2. find out ways that the two G's are ALWAYS together.

So, now we effectively have 5 letters because the two G's are always together. Total number of arrangements is simply 5!

6!/2! - 5! = 360 - 120 = 240

how did i do?

Sincerely
Praet
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

Praetorian's solution is correct.
6!/2! - 5!
Senior Manager
Joined: 07 Oct 2003
Posts: 358
Location: Manhattan
Followers: 2

Kudos [?]: 8 [0], given: 0

Re: Comb/Perm [#permalink]  12 Jun 2004, 15:21
Praetorian wrote:
jjomalls wrote:
The word NUGGET has six letters.

What is the maximum # of different arrangement of character strings (e.g. GETNGU) one can make, ensuring that the two G letters are at least one letter apart?

i might just screw this up..so study the solution and let me know.

1. find out number of arrangements of NUGGET ( no restrictions)

6!/2! is the total number of ways ( remember the signals problem, we have to divide by 2! to take care of the repitition of G)

2. find out ways that the two G's are ALWAYS together.

So, now we effectively have 5 letters because the two G's are always together. Total number of arrangements is simply 5!

6!/2! - 5! = 360 - 120 = 240

how did i do?

Sincerely
Praet

Could someone explain why is it that 5! indeed represents the number of ways to have 2 G's always together? any explanation would be greatly appreciated.
Manager
Joined: 02 Jun 2004
Posts: 154
Location: san jose,ca
Followers: 3

Kudos [?]: 18 [0], given: 0

lastochka,
just bundle the two G's together with a rope and now you have 5 items (E T N U and one bundle ).Arrangement of 5 items can be done in 5! ways (this is the basic theorem).

Hope this helps.

Agree with Praet's solution.
_________________

GS
No excuses - Need 750!!!

Manager
Joined: 07 May 2004
Posts: 183
Location: Ukraine, Russia(part-time)
Followers: 2

Kudos [?]: 8 [0], given: 0

Re: Comb/Perm [#permalink]  13 Jun 2004, 02:48
jjomalls wrote:
The word NUGGET has six letters.

What is the maximum # of different arrangement of character strings (e.g. GETNGU) one can make, ensuring that the two G letters are at least one letter apart?

total # of combinations: 6!/2

GG****, *GG***, **GG**, ***GG*, ****GG are not allowed: 5*4!.

The answer is 6!/2 - 5*4! = 240.
Re: Comb/Perm   [#permalink] 13 Jun 2004, 02:48
Similar topics Replies Last post
Similar
Topics:
1 What fraction of seven lettered words formed using the lette 1 12 May 2014, 22:44
What fraction of seven lettered words formed using the 1 02 Nov 2012, 13:37
Arrange letters of the word 6 20 May 2011, 05:55
From the word TRAMPLE 4 letters are taken. What is the 9 25 Oct 2005, 03:45
4 letters are randomly selected from the word TRAMPLE. What 5 01 Oct 2005, 21:46
Display posts from previous: Sort by