Question
In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?
Answer: Option C
Taking the vowels (EA) as one letter, the given word has the letters XTR (EA), i.e., 4 letters.
These letters can be arranged in 4! = 24 ways
The letters EA may be arranged amongst themselves in 2 ways.
Number of arrangements having vowels together = (24 × 2) = 48 ways
Total arrangements of all letters
= 5!
= (5 × 4 × 3 × 2 × 1)
= 120
Number of arrangements not having vowels together
= (120 - 48)
= 72
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Taking the vowels (EA) as one letter, the given word has the letters XTR (EA), i.e., 4 letters.
These letters can be arranged in 4! = 24 ways
The letters EA may be arranged amongst themselves in 2 ways.
Number of arrangements having vowels together = (24 × 2) = 48 ways
Total arrangements of all letters
= 5!
= (5 × 4 × 3 × 2 × 1)
= 120
Number of arrangements not having vowels together
= (120 - 48)
= 72
Was this answer helpful ?
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