In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?	Pick:  A) 800  B) 880  C) 720  D) 1500  E) 1110
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!=5×4×3×2×1=120   All the 3 vowels (OIA) are different   Number of ways to arrange these vowels among themselves   =3!=3×2×1=6   Hence, required number of ways   =120×6=720   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?