In how many different ways, can the letters of the words EXTRA be arranged so that the vowels are never together ?
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 $$2!=2$$ ways.
Number of arrangements having vowels together = $$(24 \times 2) = 48$$ ways
Total arrangements of all letters = $$5!=120$$ ways
=> Number of arrangements not having vowels together = $$(120 - 48) = 72$$ ways
=> Ans - (D)
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