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 = \(\frac{5!}{2!}\) = 60
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 = \(\frac{3!}{2!}\) = 3
Number of words where vowels are together = 6 x 3 = 18
⇒ Number of words where vowels are not together = 60 - 18 = 42
There are 42 words where vowels are not together
