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21 Apr 2022, 05:15
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:
25%
(medium)
Question Stats:
67% (00:56) correct
33%
(01:37)
wrong
based on 91
sessions
History
Date
Time
Result
Not Attempted Yet
How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together ?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 120
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 36
(B) 48
(C) 72
(D) 96
(E) 120
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
22 Apr 2022, 06:31
Kudos
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Easiest way will be to take the total number of arrangements minus the total number of arrangements in which the vowels are together.
Total number of arrangements: \(5! = 120\)
Total number of arrangements where the vowels are together: Grouping the vowels as a single letter (ie. [a+e], x, t, r) will give the total number of arrangements where the vowels are together.
\(4! *2 = 48\). Multiplying by 2 includes both 'ae' and 'ea' variations.
Number of arrangements where the vowels are not together: \(120 - 48 = 72 \)
Answer C
Total number of arrangements: \(5! = 120\)
Total number of arrangements where the vowels are together: Grouping the vowels as a single letter (ie. [a+e], x, t, r) will give the total number of arrangements where the vowels are together.
\(4! *2 = 48\). Multiplying by 2 includes both 'ae' and 'ea' variations.
Number of arrangements where the vowels are not together: \(120 - 48 = 72 \)
Answer C
SandeepReddy26
25 Apr 2022, 20:37
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We can arrange 5 letters of the word EXTRA in 5! = 120 ways.
next, we have to consider the cases where both the vowels are together i.e., 4!*2! as the vowels can be arranged among themselves in 2! ways.
Therefore, total number of words where the vowels are not together is 120-48 = 72.
next, we have to consider the cases where both the vowels are together i.e., 4!*2! as the vowels can be arranged among themselves in 2! ways.
Therefore, total number of words where the vowels are not together is 120-48 = 72.
