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

Correct Answer: (4! x 3!) / 2!

Explanation:

ABACUS is a 6 letter word with 3 of the letters being vowels.


 


If the 3 vowels have to appear together, then there will 3 other consonants and a set of 3 vowels together.


 


These 4 elements can be rearranged in 4! Ways.


 


The 3 vowels can rearrange amongst themselves in 3!/2! ways as "a" appears twice.


 


Hence, the total number of rearrangements in which the vowels appear together are (4! x 3!)/2!


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