Question 10

In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

Solution

ABACUS 
Vowels = AAU 
Remaining BCS
Now AAU will be considered 1 and B,C,S separate 
so these can be arranged in 4! ways 
Vowels AAU can be arranged in 3!/2! ways 
so total arrangements = $$\frac{4!\times\ 3!}{2!}$$


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