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romitvsingh Rising GMAT Star
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permutation Post Wed Nov 23, 2011 10:10 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    shankar.ashwin GMAT Destroyer! Default Avatar
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    Post 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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