Question

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

Answer 1

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 ⁴P₃ x 1/2! ways,

Hence, the required ways = 3! x ⁴P₃ x 1/2! = 72.