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### Discussion :: Permutation and Combination

1.  In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
2.  A. 810 B. 1440 C. 2880 D. 50400 E. 5760

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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