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Re: In how many different ways can the letters of the word DESIGN be arran
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18 Jan 2022, 07:13
Carcass wrote:
In how many different ways can the letters of the word DESIGN be arranged so that the vowels are at the two ends?
(A) 24 (B) 36 (C) 48 (D) 60 (E) 72
Take the task of arranging the letters and break it into stages. DESIGN has 6 letters. So, we must place each letter in one of six spaces.
We’ll begin with the most restrictive stage.
Stage 1: Select a letter for space #1 Since this letter must be either E or I, we can complete stage 1 in 2 ways
Stage 2: Select a letter for space #6 This letter must also be a vowel. Since we already placed one of the two vowels in space #1, the remaining vowel must be placed in space #6. So, we can complete stage 2 in 1 way
Stage 3: Select a letter for space #2 There are 4 letters remaining to be placed, so we can complete stage 3 in 4 ways
Stage 4: Select a letter for space #3 There are 3 letters remaining, so we can complete stage 4 in 3 ways
Stage 5: Select a letter for space #4 There are 2 letters remaining, so we can complete stage 5 in 2 ways
Stage 6: Select a letter for space #5 There is 1 letter remaining, so we can complete stage 6 in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus arrange all 6 letters) in (2)(1)(4)(3)(2)(1) ways (= 48 ways)
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
Re: In how many different ways can the letters of the word DESIGN be arran
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20 Jun 2024, 14:13
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Re: In how many different ways can the letters of the word DESIGN be arran [#permalink]
18 Jan 2022, 06:31 
83% (00:58) correct
