Q.) How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are always together?

(a) 48

(b) 60

(c) 40

(d) 30

Solution : Since vowels have to be always together , so EA would be treated as single letter which can be arranged among itself in 2 ways.

EXTRA = 4 letters as EA would be treated as single letter.

Now, all 4 letters are distinct. Hence , it can be arranged in 4! ways .

Total number of different arrangements = 4! x 2 = 48.

Hence Option(a)

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