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Question

All the letters of the word EAMCOT are arranged in different possible ways. Find the number of arrangement in which no two vowels are adjacent to each other.

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Solution

To find no. of ways of arranging 'EAMCOT' in which no two vowels are adjacent to each other, first arrange consonants.
Vowels: E, A, D
Consonants: M, C, T
_M_C_T_ can be arranged in 3! ways
Now, fill the blanks with vowels, it can be done in 4P3 ways.
So, total no. of ways=3!×4P3
6×4!1!
144 ways.

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