# Number of different words that can be formed using all letters of word DEEPMALA if two vowels are together and other two also together but separated from first two.

No of possible arrangements of vowels = $\frac{4!}{2!2!}=6$

Now, we have to make the cases of how this word can be arranged

Case 1 : In first place there is a 2 vowel

__V___ _ _ _ _

1 4 4 3 2 1 --- No of ways = 1*4*4*3*2*1= 96

Case 2 : In second place there is a 2 vowel

_____

__V___ _ _ _

4 1 3 3 2 1 --- No of ways= 4*1*3*3*2*1=72

Case 3 : In third place there is a 2 vowel

_ _

__V___ _ _

4 3 1 2 2 1 --- No of ways=4*3*1*2*2*1=48

Case 4 : In fourth place there is a 2 vowel

______ _

__V___ _

4 3 2 1 1 1 --- No of ways=4*3*2*1*1*1=24

No more possible cases will be there as the letter will be repeated.

Thus,total ways= 96+72+48+24=240

Now, vowels can be arranged in 6 ways

Therefore, no of different words = 240 *6 =1440

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