I have a confusion in one of the examples given in the book Discrete Mathematics: Elementary and Beyond. The exercise says:
In how many ways, in a party of six guests, can the people be seated around a circular table, given that Alice [the host] can too sit anywhere?
The answer given is a baffling $7.6.5 \; ... \;1 = 5040$
In the previous example, the host was asked to fix her place as it was her birthday (but the actual reason is to establish a point of reference, isn't it?). The answer then simply was $6!$, which makes sense. But now, this consideration of circular arrangements has been discarded and the answer matches that of arranging seven people in a straight line!
Is the answer wrong or am I missing something here?