In how many different ways can the letters of the word 'CORPORATMON' be arranged so that the vowels always come together?
Choices:
A) 40000
B) 50000
C) 50400
D) 50700
E) 60000
The word 'CORPORATMON' has 11 letters. It has the vowels 'O','O','A','M','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(OOAMO).   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! = (7×6×5×4×3×2×1)/(2×1) = 2520   In the 5 vowels (OOAMO), 'O' occurs 3 and rest of the vowels are different.   Number of ways to arrange these vowels among themselves = 5!3! = (5×4×3×2×1)/(3×2×1) = 20   Hence, required number of ways = 2520 x 20 = 50400   50400
<result>C</result>
In how many different ways can the letters of the word 'CORPORATMON' be arranged so that the vowels always come together?