In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? Choose the correct option: A) 610 B) 720 C) 825 D) 920 E) 650
Explanation:   The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).   Hence we can assume total letters as 5 and all these letters are different.   Number of ways to arrange these letters   =5!=5Ã—4Ã—3Ã—2Ã—1=120=5!=5Ã—4Ã—3Ã—2Ã—1=120   All the 3 vowels (OIA) are different   Number of ways to arrange these vowels among themselves   =3!=3Ã—2Ã—1=6=3!=3Ã—2Ã—1=6   Hence, required number of ways   =120Ã—6=720   ANSWER IS 720
<result>B</result>
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?