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Updated on: 08 Jul 2015, 08:05
Originally posted by GMATinsight on 08 Jul 2015, 07:35.
Last edited by Bunuel on 08 Jul 2015, 08:05, edited 1 time in total.
Last edited by Bunuel on 08 Jul 2015, 08:05, edited 1 time in total.
Renamed the topic and edited the question.
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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:
35%
(medium)
Question Stats:
62% (01:03) correct
38%
(01:17)
wrong
based on 193
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels always appear together?
A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!
A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
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08 Jul 2015, 07:45
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GMATinsight
Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (9 letters, 5 vowels a,e,i,o,u and 4 consonants d,c,t,n)
For all vowels together, consider them as 1 group {a,e,i,o,u}, d,c,t,n --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 5! ways
Thus total arrangements with all consonants together = 5!*5! --> C is the correct answer.
10 Feb 2020, 09:16
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GMATinsight
VOWELS: E, U, A, I, O
CONSONANTS: D, C, T, N
Take the task of arranging the letters and break it into stages.
Stage 1: Arrange the 5 vowels
We can arrange n unique objects in n! ways
So, we can arrange the 5 vowels in 5! ways
In other words, we can complete stage 1 in 5! ways
Stage 2: Arrange the 4 consonants
There are 4 unique objects to arrange.
We can complete stage 2 in 4! ways
Stage 3: The two groups of letters (the vowel group and the consonant group)
There are two options:
1) CONSONANTS-VOWELS
1) VOWELS-CONSONANTS
We can complete stage 3 in 2 ways
By the Fundamental Counting Principle (FCP), we can complete the 3 stages (and thus arrange all 9 letters) in (5!)(4!)(2) ways.
Answer: D
Cheers,
Brent
