- #26

FactChecker

Science Advisor

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Ok. I would start by 1) counting it as though exact seating mattered. 2) Then divide by cases where multiple seating arrangements will be considered equivalent.

1)

There are 10 seats for 10 people. The people can be put in them in 10! ways.

2)

The seating at the small table (4 seats) will be considered equivalent if they are just rotations of each other. ABCD = BCDA = CDAB = DABC. So divide by 4.

Similarly, the seating at the large table (6 seats) will be considered equivalent if they are just rotations of each other. So divide by 6.

1)

**Counting as though exact seating matters**There are 10 seats for 10 people. The people can be put in them in 10! ways.

2)

**Divide by cases where multiple seating arrangements will be considered equivalent.**The seating at the small table (4 seats) will be considered equivalent if they are just rotations of each other. ABCD = BCDA = CDAB = DABC. So divide by 4.

Similarly, the seating at the large table (6 seats) will be considered equivalent if they are just rotations of each other. So divide by 6.

**Final answer**: 10!/(4*6).**Note**: This is the same as 10!/4! that some people got. I couldn't exactly follow the logic of the people who got 10!/4! in one step.**Note:**If clockwise and counterclockwise are also considered equivalent, then divide by 8 and 12 rather than 4 and 6.
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