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The letters D, G, I, I , and T can be used to form 5-letter
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25 Aug 2020, 07:50
25 Aug 2020, 07:50
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Question Stats:
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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
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A) 12
B) 18
C) 24
D) 36
E) 48
_________________
Re: The letters D, G, I, I , and T can be used to form 5-letter
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25 Aug 2020, 07:50
25 Aug 2020, 07:50
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Re: The letters D, G, I, I , and T can be used to form 5-letter
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25 Aug 2020, 08:02
25 Aug 2020, 08:02
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Different ways in which DGIIT can be arranged: 5! / 2!
ways in which DGIT can be arranged (considering II as 1 letter): 4!
Ways in which DGIIT can be arranged such that II are not together : 5!/2! - 4! = 60 -24 = 36
ways in which DGIT can be arranged (considering II as 1 letter): 4!
Ways in which DGIIT can be arranged such that II are not together : 5!/2! - 4! = 60 -24 = 36
Re: The letters D, G, I, I , and T can be used to form 5-letter
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25 Aug 2020, 08:43
25 Aug 2020, 08:43
Carcass 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
A) 12
B) 18
C) 24
D) 36
E) 48
One approach.
Take the task of arranging the 5 letters and break it into stages.
Stage 1: Arrange the 3 CONSONANTS (D, G and T) in a row
We can arrange n unique objects in n! ways.
So, we can arrange the 3 consonants in 3! ways (= 6 ways)
So, we can complete stage 1 in 6 ways
IMPORTANT: For each arrangement of 3 consonants, there are 4 places where the two I's can be placed.
For example, in the arrangement DTG, we can add spaces as follows _D_T_G_
So, if we place each I in one of the available spaces, we can ENSURE that the two I's are never together.
Stage 2: Select two available spaces and place an I in each space.
Since the order in which we select the two spaces does not matter, we can use combinations.
We can select 2 spaces from 4 spaces in 4C2 ways (= 6 ways)
So we can complete stage 2 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus arrange all 5 letters) in (6)(6) ways (= 36 ways)
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So be sure to learn this technique.
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Re: The letters D, G, I, I , and T can be used to form 5-letter
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13 Jan 2023, 10:40
13 Jan 2023, 10:40
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