Number of different words that can be formed using all the letters of the word 'DEEPMALA' if two vowels are together and the other two are also together but separated from the fist two is

Explanation

We have letters D, P,M,L,E,E,A,A.
We first arrange consonat D,P,M,L in 4 ways.
`xxDxxPxxMxxLxx`
According to the question we have to put two pairs of vowels in the places marked with `xx`. For that two places can be selected in ` .^(5)C_(2)` ways. In these two places we have to arrange letters E,E,A, A which can be done in `(4!)/(2!2!)`.
So, total number of words `=4!xx .^(5)C_(2)xx(4!)/(2!2!)=1440`