Question 10

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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