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

• A. 360
• B. 114
• C. 72
• D. 54

Answer 1

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 ${}^4{P}_3\times \frac{1}{2!}$ ways.
Hence the required number $=3!{\times }^4{P}_3\times \frac{1}{2!}=72$