Discussion :: Permutation and Combination

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Answer : Option D
Explanation :
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 = \(\frac { 7! } { 2 !} \)=2520
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in\(\frac { 5! } { 3! } \)=20 ways
Required number of ways = (2520 x 20) = 50400.
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