In how many different ways can the letters of the word 'COMPUTER' be arranged in such a way that the vowels always come together?
The word 'COMPUTER' has 8 different letters. When the vowels OUE are always together, they can be supposed to form one letter. Then, we have to arrange the letters CMPTR (OUE). Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways. The vowels (OUE) can be arranged among themselves in 3! = 6 ways. Required number of ways = (720 x 6) = 4320
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