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

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Manager
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The word NUGGET has six letters. What is the maximum # of [#permalink]

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24 May 2004, 08:10
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?
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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
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24 May 2004, 18:05
Praetorian's solution is correct.
6!/2! - 5!
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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.
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12 Jun 2004, 16:55
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.
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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
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