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26 Aug 2022, 04:20
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (03:05) correct
62%
(03:08)
wrong
based on 84
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can the letters of the word MATHEMATICS can be arranged such that no two vowels are together?
A. 15,120
B. 1,058,400
C. 2,116,800
D. 4,233,600
E. 8,467,200
Fresh GMAT Club Tests' Question
A. 15,120
B. 1,058,400
C. 2,116,800
D. 4,233,600
E. 8,467,200
Fresh GMAT Club Tests' Question
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27 Aug 2022, 09:54
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Number of ways of arranging the consonants: \(\frac{7!}{2!2!}\)
Number of ways of arranging the vowels: \(\frac{4!}{2!}\)
Using placeholders for the consonants and spaces for vowels [numbers will depict consonants and () will depict empty spaces where vowels can slot into]:
\(()1()2()3()4()5()6()7()\)
Counting the spaces one finds that there are 8 possible spaces where the 4 vowels can go without being next to one another. The number of ways to choose 4 spaces out of 8: \(\frac{8!}{4!4!}\)
Which means that the total number of ways in which 'MATHEMATICS' can be arranged without two vowels being next to one another is: \(\frac{7!}{2!2!}*\frac{4!}{2!}*\frac{8!}{4!4!}\)
\(= 1260*12*70\)
\(= 1 058 400\)
Answer B
Number of ways of arranging the vowels: \(\frac{4!}{2!}\)
Using placeholders for the consonants and spaces for vowels [numbers will depict consonants and () will depict empty spaces where vowels can slot into]:
\(()1()2()3()4()5()6()7()\)
Counting the spaces one finds that there are 8 possible spaces where the 4 vowels can go without being next to one another. The number of ways to choose 4 spaces out of 8: \(\frac{8!}{4!4!}\)
Which means that the total number of ways in which 'MATHEMATICS' can be arranged without two vowels being next to one another is: \(\frac{7!}{2!2!}*\frac{4!}{2!}*\frac{8!}{4!4!}\)
\(= 1260*12*70\)
\(= 1 058 400\)
Answer B
General Discussion
23 Apr 2026, 12:18
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well i tried ;
total no. of possible arrangements of the given word MINUS the arrangements where all the vowels are together but landed at almost 4 times the correct answer.
still wondering why????
HELP
total no. of possible arrangements of the given word MINUS the arrangements where all the vowels are together but landed at almost 4 times the correct answer.
still wondering why????
HELP
