Question

The number of ways in which we can form a 8 letter word from the letters of the word daughter such that all the vowels are never together

Answer 1

The number of ways in which they are all together is 6!×3!=4320. The total number of ways to arrange DAUGHTER is 8!=40320, so the number of ways to avoid the 3 vowels being together is 40320−4320=36000.