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 $= (120*6) = 720$.