Question

All the letters of the word ïEAMCOTÍ are arranged in different 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

(B) is the correct choice.
We note that there are 3 consonants and 3 vowels E, A and O. Since no two vowels have to be together, the possible choice for vowels are the places marked as ‘X’.
X M X C X T X, these vowels can be arranged in 4P3 ways 3 consonants can be arranged in 3 ways.
Hence, the required number of ways = 3! × 4P3 = 144