In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Choose the correct answer:  A) 54000  B) 50400  C) 40500  D) 45000  E) None of them
In the word 'CORPORATION', we treat the vowels OOAIO as one letter.   Thus, we have CRPRTN (OOAIO).   This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.   Number of ways arranging these letters = 7!/2! = 2520.   Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged   in 5!/3!= 20 ways.   Required number of ways = (2520 x 20) = 50400.   Answer is 50400.
<result>B</result>
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?