IV. The numbers of permutations of N distinct objects arranged in a circle is (n-1)!

The Question: Why is it that in a circle the formula to be use is (n-1)! why -1?

Spoiler:

I did not quite understand this thread thats why I started mine.
http://www.mathhelpforum.com/math-he...rmutation.html

2. Originally Posted by networkmancer
IV. The numbers of permutations of N distinct objects arranged in a circle is (n-1)!

The Question: Why is it that in a circle the formula to be use is (n-1)! why -1?
It we are to line-up N people then it is easy to see there are $N!$ ways to do it.

But sitting N people around a table there is no starting (left-hand most) person.
If we wanted to we could designate a ‘starting’ person in N ways.
Thus there are only $\frac{N!}{N}=(N-1)!$ different ways to do this.

Here is another way to look at this problem.
At a circular table with N seats, pick one to be the head of the table.
Select one person to be seated there.
Now there are $N-1$ people left.
Starting at the right-hand side of the head-seat, there are $(N-1)!$ ways to seat the remaining people.

3. Thanks a lot for the quick reply. Now I know . Nice forum BTW.

+REP!