The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible?

Think of it as filling 12 boxes with twelve objects.

There are 12 different ways of filling the first box. When we move on to the second box, one object is in the first box, thus leaving us with 11 objects --> 11 different ways of filling the second box. This process continues on until there is only 1 way we can fill the 12th box. Thus the total number of ways to fill 12 boxes with 12 different objects is 12! = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600.

Now, this implies that there are 12! = 479,001,600 different seating arrangements.

Does this make sense?

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