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In how many ways can the letters D, I, G, I, T be arranged so that the

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Question Stats:

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In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-letters- ... 20320.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Oct 2017, 06:34, edited 2 times in total.
added oa, format, source!

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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New post 21 Apr 2010, 03:55
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sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

[Reveal] Spoiler:
36

total number of ways to arrange all the letters = 5!/2!
this includes when both I's are together and not together.
now consider both I's are combined together and arranged, then total number = 4!
these are the arrangements when both the I's are together.

so number of ways when both I's are not together = 5!/2! - 4! = 60-24 = 36

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128


OA:

First, find the number of total choices: the number of ways to arrange 5 letters of which 2 are identical equals the number of arrangements for 5 different letters divided by the number of internal arrangements of the 2 identical letters (which we don't want to count, since they do not yield distinct arrangements):

Next, find the number of Forbidden choices (in which the 2 I's are next to each other) - treat the 2 I's as one, so you have to arrange only 4 terms (3 different digits plus one "big" digit of two Is): that's 4! options.

Note: since the two I's are identical, you need NOT multiply that by the number of internal arrangements of the I's (2!)

Finally, find the number of Good choices:

60 - 4! = 60-24 = 36
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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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New post 05 Aug 2015, 14:14
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sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128


1 D
2 I
1 G
1 T

Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60

Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGT = 4! = 24

Total allowed cases = 60-24 =36

A is the correct answer.

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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New post 07 Dec 2016, 20:19
We only care about the two I's, so we can do the following:

5C3 = 10 --> total number of combinations we can have with the two I's

*take 4 away from this number because those are all of the combinations that have the two i's next to each other

Next, when the two i's are in a combination, we have 3x2x1 = 6 ways to arrange the other 3 letters --> thus for each of the 6 combinations for the two i's, we have 6 ways to arrange the other letters --> 6x6 = 36

A.

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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New post 12 May 2017, 22:03
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Bunuel: Please untag probabilty
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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New post 13 May 2017, 01:09

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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New post 01 Aug 2017, 06:37
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Engr2012 wrote:
sudai wrote:
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?

A. 36
B. 48
C. 72
D. 96
E. 128


1 D
2 I
1 G
1 T

Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60

Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGT = 4! = 24

Total allowed cases = 60-24 =36

A is the correct answer.


But cant we consider 4! * 2 as the two Is considered can be arranged in two ways?

mike Bunuel can you guys help me?

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Re: In how many ways can the letters D, I, G, I, T be arranged so that the [#permalink]

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New post 06 Oct 2017, 06:34

Kudos [?]: 132894 [0], given: 12391

Re: In how many ways can the letters D, I, G, I, T be arranged so that the   [#permalink] 06 Oct 2017, 06:34
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