BTGmoderatorLU wrote:In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
A. 6!/2!
B. 3!*3!
C. 4!/2!
D. 4!*3!/2!
E. 3!*3!/2!
Since the vowels must appear together, put them together in a BLOCK: [AAU].
Now count the number of ways to arrange the 4 elements [AAU], B, C and S.
The number of ways to arrange 4 distinct elements = 4!.
Now we must account for the number of ways that the vowels themselves can be arranged WITHIN the [AAU] block.
The vowels can be arranged as follows:
AAU, AUA, UAA.
Total ways = 3.
Multiplying the results above, we get:
4! * 3.
This is the value yielded by answer choice
D:
(4! * 3!)/2! = 4! * 3.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
