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permutation

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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permutation

by romitvsingh » Wed Nov 23, 2011 10:10 pm
In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

A 6!/2!

B. 3! * 3!
C. 4!/2!
D. 4!*3!/2!
E. 3!*3!/2!
PLS explain in detail
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by shankar.ashwin » Wed Nov 23, 2011 11:08 pm
ABACUS has 3 vowels (2 A's and 1 U)

AAU can be arranged among themselves in 3!/2! ways

Consider the vowels to be in one group in any order (AAU) and other 3 consonants are B,C and S.

Now there are 4 different entities and they can be arranged in 4! ways.

Coming to include combinations of vowels within themselves (AAU and so on), we multiply.

So, 4!*3!/2! D IMO
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