# GMAT Quant Questions | GMAT Permutation Q1

#### Combinatorics | Reordering, Rearrangement | GMAT Sample Questions

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?

1. $$frac{6!}{2!}$ 2. 3! × 3! 3. $\frac{4!}{2!}$ 4. $\frac{4! \times 3!}{2!}$ 5. $\frac{3! \times 3!}{2!}$ ## Get to 705+ in the GMAT #### Online GMAT Course @ INR 8000 + GST ### Video Explanation ## GMAT Live Online Classes #### Starts Sat, July 20, 2024 ### Explanatory Answer | GMAT Permutation Combination Q1 #### Step 1 of solving this GMAT Permutation Question: Group the vowels as one unit and rearrange 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. #### Step 2 of solving this GMAT Permutation Question: 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 of the word ABACUS in which the vowels appear together is $\frac{4! \times 3!}{2!}$ #### Choice D is the correct answer. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch July 20, 2024 Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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