This sample GMAT Math question is a 600 level combinatorics problem solving question. The concept tested is to find the number of ways the letters of word can be rearranged after factoring in constraints that a certain type of letters should be grouped together. An elementary permutation question on rearragements and reordering objects.

Question 1: 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! \times 3!}{2!})
- \\frac{3! \times 3!}{2!})

From INR

ABACUS is a 6 letter word in which 3 of the letters are vowels, viz., A, A, and U.

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.

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

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

Copyrights © 2016 - 23 All Rights Reserved by Wizako.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

GMAT^{®} is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.

GRE^{®} is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.

SAT^{®} is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.

Wizako - GMAT, GRE, SAT Prep

An Ascent Education Initiative

14B/1 Dr Thirumurthy Nagar 1st Street

Nungambakkam

Chennai 600 034. India

**Mobile:** (91) 95000 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@wizako.com

Leave A Message