Question

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

Options

• 810

• 1440

• 2880

• 50400

Answer 1

50400
Explanation:

In the word 'CORPORATION', we treat the vowels OOAlO 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

`(5!)/(3!)=20` ways

∴ Required number of ways
= (2520 x 20) = 50400