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All the letters of the word EAMCET are arranged in all possibl

Question

All the letters of the word $E A MCET$ are arranged in all possible ways. The number of such arrangements in which no two vowels are adjacent to each other is

36

54

72

144

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All the letters of the word

E A MCET

are arranged in all possible ways. The number of such arrangements in which no two vowels are adjacent to each other is

15 mins ago

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Text solutionVerified

Vowels are

E, A, E

and consonants are

M, C, T

For two vowels not to come adjacent, first of all arrange the

3

consonants in

3!

ways in a line leaving the adjacent sides vacant.

Now these

3

consonants will have

4

vacant spaces, and we have

3

vowels

So we can select

3

vacant spaces for vowel in

^{4} C_{3}

ways and then arrange them in

\frac{3 !}{2 !}

ways. ( since

E

is repeated )

Hence required number of word will be

= 3! \cdot^{4} C_{3} \cdot \frac{3 !}{2 !} = 72

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Question Text	All the letters of the word $E A MCET$ are arranged in all possible ways. The number of such arrangements in which no two vowels are adjacent to each other is
Answer Type	Text solution:1
Upvotes	150

All the letters of the word EAMCET are arranged in all possible ways. The number of such arrangements in which no two vowels are adjacent to each other is

Text solutionVerified

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All the letters of the word $E A MCET$ are arranged in all possible ways. The number of such arrangements in which no two vowels are adjacent to each other is