In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? In the below solved problem, every thing is okay, but if we have $4$ consonants then why we are giving $5!$? and is this a combination problem? how to distinguish?

Question:
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? 

Answer:
The word 'OPTICAL' contains $7$ different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, $5$ letters can be arranged in $5! = 120$ ways.
The vowels (OIA) can be arranged among themselves in $3! = 6$ ways.
Required number of ways $= (120*6) = 720$.
There are $4$ consonants and $1$ group of vowels, so there are $5$ elements to permute. Yes, this is a combinatorial problem because we are counting the number of possibilities that satisfy certain conditions.
For this problem I use the multinomial coefficient.
We have 7 letters in total 3 of which are vowels and 4 are consonants
The number of vowels combinations are 3! and the number of consonants combinations are 4! (I've used the multinomial coefficient)
So by the end we've 3!*4! ways