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

In how many ways can the letters of the word ABACUS be rearranged such that thevowels always appear together? Correct Answer (4! x 3!) \/ 2!

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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