Question 1209585
<pre>
Round table problems always falsely assume that the round table is placed on a
huge turntable. That's not the way it is in reality, but that's the way it is
always assumed to be in all round table problems in all algebra books I've ever
seen in all my 40+ years of teaching math. Thus for any seating arrangement,
turning the turntable in any direction does not alter the seating arrangement.  

There are 10 people. [It makes no difference whether they are students, female
teachers, or male teachers].  Choose 1 person to sit facing north.

[Remember, it doesn't matter which person sits facing north at first, because
the turntable could be turned so that anybody could face north. So even though
that person could be picked to face north at first 10 ways, it does not matter
which person you pick. So be sure not to think you could pick that person 10
ways.

(If you did choose that person 10 ways, you'd then have to divide that 10 by the
10 ways to turn the turntable so that each of the 10 would have a chance to be
facing north, so it's just 1 choice to choose somebody to sit facing north.)]

Then seat the other 9 people in the other 9 chairs in 9! ways. 

Answer 9! = 362880 ways.

Edwin</pre>