Question

All the letters of the word ‘EAMCET’ are arranged in all possible ways. The number of such arrangement in which two vowels are not adjacent to each other is

• A. 360
• B. 114
• C. 72
• D. 54

Answer 1

Answer: (C)

72

Answer 2

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 $4P_{3} \times \frac{1}{2!}$ ways.

Hence the required ways = 3 ! × $4P_{3} \times \frac{1}{2!} = 72$.