Question
In how many different ways can the letters of the word `CORPORATION` be arranged so that he vowels always come together ?
Answer: Option D
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In he word `CORPORATION` we treat the vowels OOAIO as one letter. Thus we have CRPRTN(OOAIO).
This has 7 letters of which R occurs 2 times and the rest are different .
Number of ways of 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.
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