How many arrangements can be made out of the letters of the word DRAUGHT, the vowels never being separated?

There are 7 letters in the word DRAUGHT, the two vowels are A and U.
Since, the vowels are not to be separated; AU can be considered as one entity.
Therefore, the number of letters will be 6 instead of 7.
The permutations will be P(6,6) = 6! ways.
But the two vowels A and U can be arranged in two ways, i.e. AU and UA.
The required number of arrangements = 2!.6! = 1440 ways.