BTGModeratorVI wrote: ↑Sun Jul 26, 2020 6:38 am
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
Answer:
D
Source: Official guide
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 GMAT. For more information about the FCP, watch this video:
https://www.gmatprepnow.com/module/gmat- ... /video/775
You can also watch a demonstration of the FCP in action:
https://www.gmatprepnow.com/module/gmat ... /video/776
Then you can try solving the following questions:
EASY
-
https://www.beatthegmat.com/what-should- ... 67256.html
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https://www.beatthegmat.com/counting-pro ... 44302.html
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https://www.beatthegmat.com/picking-a-5- ... 73110.html
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https://www.beatthegmat.com/permutation- ... 57412.html
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https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
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https://www.beatthegmat.com/combinatoric ... 73194.html
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https://www.beatthegmat.com/arabian-hors ... 50703.html
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https://www.beatthegmat.com/sub-sets-pro ... 73337.html
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https://www.beatthegmat.com/combinatoric ... 73180.html
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https://www.beatthegmat.com/digits-numbers-t270127.html
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https://www.beatthegmat.com/doubt-on-sep ... 71047.html
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https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
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https://www.beatthegmat.com/wonderful-p- ... 71001.html
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https://www.beatthegmat.com/permutation- ... 73915.html
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https://www.beatthegmat.com/permutation-t122873.html
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https://www.beatthegmat.com/no-two-ladie ... 75661.html
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https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
