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

nice method

To find the number of different words that can be formed using the letters of the word "DEEPMALA" with two vowels together and the other two vowels separated from the first two, we can follow these steps:

Step 1: Count the number of vowels and consonants in the given word.
In this case, the word is "DEEPMALA". The vowels are E, E, A, and the consonants are D, P, M, L. So our count is 4 vowels and 4 consonants.

Step 2: Determine the number of ways to arrange the vowels.
Since we want two vowels together and the other two vowels separated from the first two, we can consider the pair of vowels (EE) as one unit. Now we have 3 units: (EE), A, D, P, M, L. The number of ways to arrange the 3 units is 3!, which is equal to 6 (since there are 3 units, we perform a factorial 3! = 3 x 2 x 1 = 6).

Step 3: Determine the number of ways to arrange the consonants.
We have 4 consonants: D, P, M, L. The number of ways to arrange them is 4!, which is equal to 24.

Step 4: Find the total number of words.
To find the total number of words, we multiply the number of ways to arrange the vowels (6) with the number of ways to arrange the consonants (24).
Total number of different words = 6 x 24 = 144.

Therefore, there are 144 different words that can be formed using the letters of the word "DEEPMALA" if two vowels are together and the other two are also together but separated from the first two.

Bad

These are the 6 ways to pair up the vowels:

AA EE
AE AE
AE EA
EA EA
EA AE
EE AA

Now consider the ways if you use each pair as a single letter.

But consider duplicates.