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Question

Consider the letters of the word MATHEMATICS.
Possible number of words in which no two vowels are together is

A
7! 8C4 4!2!
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B
7!2! 8C4 4!2!
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C
7!2!2! 8C4 4!2!
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D
7!2!2!2! 8C4 4!2!
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Solution

The correct option is C 7!2!2! 8C4 4!2!
Consonants have 8 gaps when arranged in a row. Consonants can be arranged in 7!2!2! ways. Then there are 8 places and 4 vowels
Therefore, number of ways is 7!2!2! 8C4 4!2!.

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