Put the O in the first place and arrange the other 5
Put the O in the last place and arrange the other 5
Add them and subtract from the total number of arrangements.
Hello, Bartimaeus!
Another approach . . .
From the word STUDIO, how many arrangements are possible
if the letter O is not the first or the last?
If the O is not first or last, there are 4 places for it: .
Then the other 5 letters can be placed in: . ways.
Therefore, there are: . arrangements.
I got the same thing by doing it the way I mentioned.
Place the O on the end and arrange the other 5 in 120 ways.
Place the O in the front and arrange the other 5 in 120 ways.
That is 240 ways.
There are 6!=720 arrangements altogether.
So, 720-240=480 ways