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Question

All the letters of the word ‘EAMCET’ are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is
  1. 360
  2. 114
  3. 72
  4. 54


Solution

The correct option is C 72
First, we arrange 3 consonants in 3! ways and then at four places (two places between them and two places on two sides) 3 vowels can be placed in 4P3×12! ways.
Hence the required number =3!×4P3×12!=72

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