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11 Jan 2022, 03:15
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
86% (00:58) correct
14%
(00:55)
wrong
based on 76
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 24
(B) 36
(C) 48
(D) 60
(E) 72
11 Jan 2022, 08:37
Kudos
Bookmarks
Bunuel
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 GMAT. So, be sure to learn it.
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