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

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Intern
Joined: 08 Jan 2015
Posts: 28
How many different possible arrangements can be obtained from the lett [#permalink]

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30 Mar 2015, 10:30
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62% (02:00) correct 38% (02:55) wrong based on 110 sessions

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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
[Reveal] Spoiler: OA
Director
Joined: 07 Aug 2011
Posts: 578
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Re: How many different possible arrangements can be obtained from the lett [#permalink]

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30 Mar 2015, 10:36
3
KUDOS
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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Lucky

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Intern
Joined: 08 Jan 2015
Posts: 28
Re: How many different possible arrangements can be obtained from the lett [#permalink]

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30 Mar 2015, 10:43
Could you explain me in detail why B is 6! / 2! ?

Thank you.
Director
Joined: 07 Aug 2011
Posts: 578
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Re: How many different possible arrangements can be obtained from the lett [#permalink]

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30 Mar 2015, 11:06
1
KUDOS
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 !
_________________

Thanks,
Lucky

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Kindly press the to appreciate my post !!

SVP
Joined: 06 Nov 2014
Posts: 1904
Re: How many different possible arrangements can be obtained from the lett [#permalink]

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31 Mar 2015, 01:50
1
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2
This post was
BOOKMARKED
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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Intern
Joined: 08 Jan 2015
Posts: 28
Re: How many different possible arrangements can be obtained from the lett [#permalink]

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31 Mar 2015, 01:56
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!
Manager
Joined: 24 May 2013
Posts: 85
Re: How many different possible arrangements can be obtained from the lett [#permalink]

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19 Mar 2016, 11:04
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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Joined: 09 Sep 2013
Posts: 13787
Re: How many different possible arrangements can be obtained from the lett [#permalink]

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07 Feb 2018, 18:17
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Re: How many different possible arrangements can be obtained from the lett   [#permalink] 07 Feb 2018, 18:17
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# How many different possible arrangements can be obtained from the lett

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