This sample GMAT Math question is a combinatorics problem solving question. The concept tested is to find the number of ways the letters of word can be rearranged after factoring in the constraint that certain category of letters should be grouped together. An elementary permutation question.

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

- \\frac{6!}{2!}\\)
- 3! * 3!
- \\frac{4!}{2!}\\)
- \\frac{4!*3!}{2!}\\)
- \\frac{3!*3!}{2!}\\)

#### Explanatory Answer

Video explanation will be added soon#### Group the vowels as one unit and rearrange

ABACUS is a 6 letter word with 3 of the letters being vowels.

Because the 3 vowels have to appear together, let us group the AAU as one unit.

There are 3 consonants in addition to one unit of vowels.

These 4 elements can be rearranged in 4! ways.

#### Rearrange the letters within the unit containing the vowels

The 3 vowels can rearrange among themselves in \\frac{3!}{2!}\\) ways because "a" appears twice.

Hence, the total number of rearrangements in which the vowels appear together is \\frac{4!*3!}{2!}\\)

Choice D is the correct answer.

### Are you targeting Q-51 in GMAT Quant? Make it a reality!

Comprehensive Online classes for GMAT Math. 20 topics.

Focused preparation for the hard-to-crack eggs in the GMAT basket!