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 =
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
No of possible arrangements of vowels =
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