Question

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

Answer 1

The vowels are never being separated.

So, vowels $a$ & $u$ are taken together and considered as one letter.

So, there are $6$ letters in the word $draught$

The number of ways in which it can be arranged are given by $=6!=720$.

But the internal arrangement can be done of $a$ and $u$ in $2$ ways.

Hence the total arrangements are $720\times 2=1440$.