(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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)

2. Relevant equations

3. 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.

**Physics Forums - The Fusion of Science and Community**

# Further Premutation / Combination problem

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

- Similar discussions for: Further Premutation / Combination problem

Loading...

**Physics Forums - The Fusion of Science and Community**