/sci/ - Science & Math

/sci/ I have a question.
(Also, some of you might say this is a homework thread. It's not actually homework, it's just something I don't understand.)

"Find how many arrangements of "n" people around a circle are possible if two particular people must sit apart."

Now, from what I know, to do that you would find the number of arrangements of two people sitting together and subtract that from the total number of arrangements. i.e. (n-1)!-2(n-2)!

BUT the book says the answer is actually (n-3)*(n-2)!. Can someone explain?

(pic. unrelated.)

/thread

A thanks is nice somethings

>>1367423
for the record, this is my personal favorite. I'm kinda an /x/ guy down under