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25 Aug 2022, 04:53
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (03:35) correct
38%
(03:24)
wrong
based on 8
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can the letters of the word MANHATTAN can be arranged such that no two vowels are together?
A. 4200
B. 6300
C. 8400
D. 10500
E. 12600
(adapted from gmatfree)
A. 4200
B. 6300
C. 8400
D. 10500
E. 12600
(adapted from gmatfree)
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25 Aug 2022, 05:33
Kudos
Bookmarks
pintukr
In the word MANHATTAN there are three vowels (A, A, and A) and six consonants (M, H, T, T, N, and N) .
Consider 6 consonants (C) of the word MANHATTAN as shown below:
*C*C*C*C*C*C*
Now, if 3 A's occupy places of any 3 stars (*) out of 7, then no two vowels will be together (there always will be at least one consonant (C) between two vowels).
In how many way we can choose 3 places out of 7? In \(C^3_7=\frac{7!}{4!3!}=35\) ways.
Three A's can be arranged in their slots in one way only, but six consonants (M, H, T, T, N, and N) can be arranges in \(\frac{6!}{2!2!} = 180\) ways.
So, the final answer is 35*180 = 6300.
Answer: B.
Archived Topic
Hi there,
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