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Permutation and Combination - August 12, 2005

The GMAT Sample Math question for the day is from the topic Permutation and Combination.

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

A.
B. 3!*3!
C.
D.
E.
The correct choice is (D) and the correct answer is .

Explanatory Answer
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 ways as "a" appears twice.
Hence, the total number of rearrangements in which the vowels appear together are

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