Arithmetic Ability
Permutations and Combinations

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Q.

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

View Answer

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