- #1
kenny1999
- 235
- 4
Homework Statement
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
(This is a question with solution I find on web, but I don't understand the solution)
Homework Equations
The Attempt at a Solution
The following is the modal answer to the problem, but I don't understand why
7! / 2! and 5! / 3!. It's very hard to think!
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 5! / 3! = 20 ways.
Required number of ways = (2520 x 20) = 50400.