Question

Discrete Math Question About Tables:

Imagine a circular table, and you want to sit 7 people around it. The total arrangements would be 7!/7 or 6!. So, the order of left or right does not matter because we can sit these people anywhere and in any direction we want.

However, If they are denoted A, B, C, D, E, F, G. Then the order matters. Thus it would be 2*(7!/7) or 2*(6!).

Am I right with my logic ? How should I know the order from left and right matters?

Answer 1

Because the circle can be rotated....

http://mathworld.wolfram.com/CircularPermutation.html

...you have \(P_n = (n-1)!\)

Answer 2

A more detailed explanation is here:

http://math.stackexchange.com/questions/2146094/discrete-math-question-about-tables/2146171?noredirect=1#comment4414908_2146171


I asked this question on math stack exchange.