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In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
ABACUSΒ
Vowels = AAUΒ
Remaining BCS
Now AAU will be considered 1 and B,C,S separateΒ
so these can be arranged in 4! waysΒ
Vowels AAU can be arranged in 3!/2! waysΒ
so total arrangements =Β $$\frac{4!\times\ 3!}{2!}$$
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