prernamalhotra wrote:Hi,
Can you please help me solve the below question:
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!
Prerna
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.
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