Permutation And Combination Question

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

Answer 1

Vowels are E,A,E and consonants are M,C,T

For two vowels not to come adjacent, first of all arrange the 3 consonants in 3! ways in a line leaving the adjacent sides vacant.

Now these 3 consonants will have 4 vacant spaces, and we have 3 vowels 

So we can select 3 vacant spaces for vowel in  ⁴C₃ ways and then arrange them in  3!/2! ways. ( since E is repeated )

Hence required number of word will be