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) 47200  B) 48000  C) 42000  D) 50400  E) 65400
Explanation:   The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).   Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.   Number of ways to arrange these letters   =7!2!=7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—12Ã—1=2520=7!2!=7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—12Ã—1=2520   In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.   Number of ways to arrange these vowels among themselves =5!3!=5Ã—4Ã—3Ã—2Ã—13Ã—2Ã—1=20=5!3!=5Ã—4Ã—3Ã—2Ã—13Ã—2Ã—1=20   Hence, required number of ways   =2520Ã—20=50400=2520Ã—20=50400   ANSWER IS 50400
<result>D</result>
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?