in how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together  Choose the correct answer:
A) 520 B) 620 C) 720 D) 750 E) 800
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 x 6) = 720.   ANSWER:720
<result>C</result>
in how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together