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Permutation and Combination

Q1: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

A 810

B 1440

C 2880

D 50400

E 5760

ANS:D - 50400

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 = 7! = 2520.
2!
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in 5! = 20 ways.
3!
 Required number of ways = (2520 x 20) = 50400.



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