Find the number of all possible different words into which the word ‘INTERFERENCE’ can be converted by change of place of the letters, it being given that no two consonants are to be together.
Answer
There is not possible to arrange a word without two consonants are to be together. because there are 12 letters in the word interference of which 5 are vowels (4 e's and 1 i) and 7 consonants (2 n's, 2 r's, and 1 each of t, f & c). There are only 6 consonants that can be placed on the sides of vowels but there are 7 consonants in the given word. So, there should be at least 1 instance where 2 consonants will come together.