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Re: In how many ways can the letters of the word GARGANTUNG be [#permalink]
2
huda wrote:

What if the letter would be ACCLAIM ?


If there are no restrictions (like all C's must be together), then we get:

ACCLAIM
There are 7 letters in total
There are 2 identical A's
There are 2 identical C's
So, the total number of possible arrangements = 7!/[(2!)(2!)]


Cheers,
Brent
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Re: In how many ways can the letters of the word GARGANTUNG be [#permalink]
GreenlightTestPrep wrote:
huda wrote:

What if the letter would be ACCLAIM ?


If there are no restrictions (like all C's must be together), then we get:

ACCLAIM
There are 7 letters in total
There are 2 identical A's
There are 2 identical C's
So, the total number of possible arrangements = 7!/[(2!)(2!)]


Cheers,
Brent


Thanks
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Re: In how many ways can the letters of the word GARGANTUNG be [#permalink]
GreenlightTestPrep wrote:
Carcass wrote:
In how many ways can the letters of the word GARGANTUNG be rearranged such that all the G’s appear together?

(A) \(\frac{8!}{3!*2!*2!}\)

(B) \(\frac{8!}{2!*2!}\)

(C) \(\frac{8!*3!}{2!*2!}\)

(D) \(\frac{8!}{2!*3!}\)

(E) \(\frac{10!}{3!*2!*2!}\)


----ASIDE--------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
---------------------------

First, "GLUE" the 3 G's together to form ONE super letter (which we'll call X)
So, we must arrange the letters in the word: ARANTUNX

There are 8 letters in total
There are 2 identical A's
There are 2 identical N's
So, the total number of possible arrangements = 8!/[(2!)(2!)]

Answer: B

Cheers,
Brent



There are 10 letters, so the answer would be 7!/2!.2!. not mentioned in any of the options...
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Re: In how many ways can the letters of the word GARGANTUNG be [#permalink]
Expert Reply
GARGANTUNG
re arranged as ; GGGARANTUN
it can be arranged as GGG as 1 ; so total 8 places
8!/2!*2! ; IMO B
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Re: In how many ways can the letters of the word GARGANTUNG be [#permalink]
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