Question

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.

Answer 1

Answer:

1440

Step-by-step explanation:

Given 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.

From the given word DEEPMALA there are 4 vowels. So number of possible ways is 4!/2!2! = 6

Now there are 2 vowels in first place = 1 x 4 x 4 x 3 x 2 x 1 = 96 ways

There are 2 vowels in 2 nd place = 4 x 1 x 3 x 3 x 2 x 1 = 72 ways

Similarly in the third place = 4 x 3 x 1 x  2 x 2 x 1 = 48 ways

In the fourth place = 4 x 3 x 2 x 1 x 1 x 1 = 24 ways

After this the letters will be repeated.

Now 96 + 72 + 48 + 24 = 240

Vowels can be arranged in 6 ways = 240 x 6 = 1440 ways