Question

In how many different ways can the letters of the word ${}^{\prime }CORPORATIO{N}^{\prime }$ be arranged so that the vowels always come together?

• A. $810$
• B. $1440$
• C. $2880$
• D. $50400$
• E. $5760$

Answer 1

The correct option is 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 = $\frac{7!}{2!}$ = 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in $\frac{5!}{3!}$ = 20 ways.
$\therefore$ Required number of ways = (2520 x 20) = 50400.