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

Question: 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

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 =	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.

Video Explanation: https://youtu.be/o3fwMoB0duw