The GMAT Sample Math question is a combinatorics problem solving question. The concept tested in this question is to find the number of ways the letters of word can be rearranged.
In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
B. 3! * 3!
The correct choice is (D) and the correct answer is
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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