To find: Number of words that can be formed so that vowels are never together

Number of words such that vowels are never the together = Total number of words - Number of words where vowels are together

Total number of words =

To find a number of words where vowels are together

Let the vowels I, I, A be represented by a single letter Z

the new word is NDZ

A number of permutations = 3! = 6

Z is composed of 3 letters which can be permuted amongst themselves.

Number of permutations of Z =

Number of words where vowels are together = = 18

Number of words where vowels are not together = 60 - 18 = 42

There are 42 words where vowels are not together