Question

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 first two is

Answer 1

Answer:

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Explanation:

DEEPMALA :  4 vowels - EEAA and 4 consonants : DPML

No of possible arrangements of vowels = 4!2! 2!=64!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