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How many different possible arrangements can be obtained from the lett

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How many different possible arrangements can be obtained from the lett [#permalink]

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New post 30 Mar 2015, 11:30
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How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

A. 360
B. 720
C. 900
D. 1800
E. 5040
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Concentration: International Business, Technology
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Re: How many different possible arrangements can be obtained from the lett [#permalink]

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New post 30 Mar 2015, 11:36
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Awli wrote:
How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

A. 360
B. 720
C. 900
D. 1800
E. 5040



A= all possible permutations = \(\frac{7!}{2!2!}\)
B= permutations with II together = \(\frac{6!}{2!}\)

A-B = 900
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Re: How many different possible arrangements can be obtained from the lett [#permalink]

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New post 30 Mar 2015, 11:43
Could you explain me in detail why B is 6! / 2! ?

Thank you.
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Re: How many different possible arrangements can be obtained from the lett [#permalink]

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New post 30 Mar 2015, 12:06
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Awli wrote:
Could you explain me in detail why B is 6! / 2! ?

Thank you.



yes sure.

we have to find those cases where we have at least 1 Character between two I I , if we find those cases where there is no character between two I I and subtract this number from total permutations we will be left with those cases where there are 1 or more characters between two I I .

assume II as one unit so we have total 6 characters G M A T T (II)
total ways to arrange these 6 letters is \(\frac{6!}{2!}\) , as we have 2 Ts so we have to divide 6! by 2! .

hope the explanation is helpful to you !
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Re: How many different possible arrangements can be obtained from the lett [#permalink]

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New post 31 Mar 2015, 02:50
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Awli wrote:
How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

A. 360
B. 720
C. 900
D. 1800
E. 5040


There are 7 letters G, M, A, T, I, I, and T with I and T repeated twice.
Hence total arrangements/permutations of letters = 7!/(2! * 2!) = 1260.

Now, let us say that the two "I" are always together.
So now we have 6 letters G, M, A, T, II, T with T repeated twice.
Hence total arrangements/permutations of letters = 6!/(2!) = 360.

Required arrangements = 1260 - 360
= 900
Hence option (C).

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Re: How many different possible arrangements can be obtained from the lett [#permalink]

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New post 31 Mar 2015, 02:56
Lucky2783 wrote:
Awli wrote:
Could you explain me in detail why B is 6! / 2! ?

Thank you.



yes sure.

we have to find those cases where we have at least 1 Character between two I I , if we find those cases where there is no character between two I I and subtract this number from total permutations we will be left with those cases where there are 1 or more characters between two I I .

assume II as one unit so we have total 6 characters G M A T T (II)
total ways to arrange these 6 letters is \(\frac{6!}{2!}\) , as we have 2 Ts so we have to divide 6! by 2! .

hope the explanation is helpful to you !



Yes, it's been very helpful. Thank you very much!
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Re: How many different possible arrangements can be obtained from the lett [#permalink]

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New post 19 Mar 2016, 12:04
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How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

_ _ _ _ _ _ _
Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's

_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!

Therefore ans = 7!/ (2!2!) -6!/2! = 900
HENCE C.

A. 360
B. 720
C. 900
D. 1800
E. 5040
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Re: How many different possible arrangements can be obtained from the lett [#permalink]

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New post 07 Feb 2018, 19:17
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Re: How many different possible arrangements can be obtained from the lett   [#permalink] 07 Feb 2018, 19:17
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