Question

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

Answer 1

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! = 2520. 2! Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5! = 20 ways. 3! Required number of ways = (2520 x 20) = 50400.