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The letters D, G, I, I , and T can be used to form 5-letter strings as

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Re: The letters D, G, I, I , and T can be used to form 5-letter strings as  [#permalink]

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New post 14 Feb 2019, 08:42
# of ways in which I's are together: 4! (glue method). Usually with the glue method need to multiply by 2, but given I's are the same, don't need to. How many total ways can "digit" be arranged with no restriction? 5! = 120. Need to divide by 2! given the repetition. 60-24 = 36
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New post 15 Feb 2019, 00:47
chetan2u
In the 2nd case ie when the 2 Is are together why are we not dividing the 4! by 2!, as the interchange of the 2 Is when they are together will lead to double the number of arrangements...
Please correct me...
Thanks in advance
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Re: The letters D, G, I, I , and T can be used to form 5-letter strings as  [#permalink]

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New post 10 Mar 2019, 20:45
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The correct answer is Choice D.

First, determine the total number of ways of rearranging the letters in DIGIT.

5! / 2! (accounts for the repetition of the 2 letter "I"s) = (5 x 4 x 3 x 2) / 2 = 120 / 2 = 60

Next, consider all the ways two letter "I"s can be adjacent within the word. They can either be in the 1/2 slot, the 2/3 slot, the 3/4 slot, or the 4/5 slot (4 locations), and for each of those 4 locations there are 3 x 2 x 1 = 6 other ways of rearranging the final 3 letters, so multiply 6 by 4 to get 24.

Subtract those 24 instances from the total to get 60 - 24 = 36

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New post 04 Jun 2019, 19:23
total number of ways that the letters can be arranged is (5!/2!) =60

it is easiest to find how many ways the I's can be together.

First we can treat both I's as a single entity ( I &I ).

This essentially this means we are arranging four entities which becomes 4!.

Thus the answer to the question is (5!/2!)- 4! = 36
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Re: The letters D, G, I, I , and T can be used to form 5-letter strings as  [#permalink]

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New post 22 Jun 2019, 06:39
@
adiagr wrote:
Bunuel wrote:
The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?

A) 12
B) 18
C) 24
D) 36
E) 48


Let us calculate the total ways. Those would be (5!/2!) = 60.

Now since the question says "at least" let us find the number of arrangements when both I's are together. (Tie them up). so we have 4! ways to arrange such that I's always come together. 4! = 24

60 - 24 = 36.

D is the answer.


I can never get this right! I always end up putting 4!*2! when i have to calculate ways of arranging DIGIT with both th I's combined, that because in my head i think both the I's can also be arranged in two ways. How do i get to correct this ! Bunuel Please help
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Re: The letters D, G, I, I , and T can be used to form 5-letter strings as   [#permalink] 22 Jun 2019, 06:39

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