Question

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

• A. 360
• B. 144
• C. 72
• D. 54

Answer 1

Answer: (C)

72

Answer 2

Gap Method. Consonants M, C, T in 3! = 6 ways and 4 gaps and 3 vowels (2 alike) in $4P_{3}.\frac{1}{2!} = 12$ways = 12 x 6 = 72