(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.

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# Further Premutation / Combination problem

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