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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
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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?
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
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
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.
Re: The letters D, G, I, I , and T can be used to form 5-letter
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19 Aug 2024, 20:43
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Re: The letters D, G, I, I , and T can be used to form 5-letter [#permalink]