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?
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.