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.

DEEPMALA :  4 vowels - EEAA and 4 consonants : DPML

No of possible arrangements of vowels = 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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