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.