How many different words can be formed using the letters of the word “EDUCATION‘ such that, All the consonants are always together ?

Sure, here is the step by step solution:

1. First, identify the consonants in the word "EDUCATION". They are D, C, T, N.

2. Since all the consonants have to be together, we can consider them as a single entity. So, the word now becomes "EUAIO(DCTN)".

3. This word has 6 entities (5 vowels and 1 group of consonants).

4. These 6 entities can be arranged in 6! ways.

5. Within the group of consonants (DCTN), the 4 consonants can be arranged in 4! ways.

6. Therefore, the total number of ways to arrange the word "EDUCATION" such that all consonants are together is 6!*4!.

7. Calculate 6!4! = 72024 = 17280.

So, 17280 different words can be formed using the letters of the word "EDUCATION" such that all the consonants are always together.