In how many ways can six applicants for a job arrange themselves around the tabl...

We solve this by pretending that the circular table is sitting on a revolving platform and the table can be turned facing any direction. If the 6 people A, B, C, D, E, and F were seated in a straight line the answer would be 6 factorial. However, if we took the 6 sample arrangements BDEFAC, DEFACB, EFACBD, FACBDE, ACBDEF, and CBDEFA, they are indistinguishable since if the people were seated in any one of them, the imaginary turntable could be turned so that any one of those 6 could be had. So we must divide by 6 and the answer is 6!/6 = 5! = 120.