In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?
Options:
A . 120
B . 48
C . 72
D . 168
E . None of these
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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