Very true, the rule is : total ways to arrange n persons around the table is (n-1)!
the example taken was
"there are 3 ppl and total way to arrange them around a table is (3-1)!=2
but I still see 3! ways. you can see here ABC, ACB, BAC, BCA, CAB, CBA"
very apt example
to explain it a further bit , firstly make it very clear that the arrangement is circular what it means is that--->
ABC , BCA, and CAB are equivalent , cause if you just pick A in any of the previous arrangements and just go on reading forward till the end you will end up reading it as ABC.
similarly ACB, BAC, and CBA are equivalent.
hence, you end up in 2 circular arrangements, that's what we got with the formula.
Peace.
:)