Getting homework done and either my mind isn't clear or I'm just overthinking this.
To get all arrangements of the 26 letters in the alphabet, it would be done by $26!$ , correct?
Okay, so I'm thinking that the five vowels (A,E,I,O,U) can be treated as one space. This means that I could find all arrangements with vowels in consecutive order by doing $22!$ .
Thinking of it as 22 blank spaces, the 22nd space is a single space made up of all five vowels while the other 21 spaces can be any other letter without repetition.
Furthermore, if I want to also include all arrangements of of the vowels as well, would this be done by $22! \cdot 5!$ ?
Thank you
We can consider that the five vowels are just one letter , so we have now 22 letters wanted to be arranged ,the number of arrangements is $$22!$$ but the number of permutations of the vowels them selves is $$5!$$ So the total ways of arrangement is $$22! \times 5!$$