Question

All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.

Answer 1

We note that, there are 3 consonants M, C, T and 3 vowels E, A, O.

Since, no two vowels have to be together, the possible choice for volwels are the blank spaces,
$\mathrm{\_M\_C\_T\_}$

These vowels can be arranged in ⁴P₃ ways.
3 consonants can be arranged in 3! ways.

Hence, the required numbers of ways = 3! × ⁴P₃ = 144 ways.