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A Senate committee has 5 Democrats and 5 Republicans. Assuming all politicians are distinguishable, in how many ways can they sit around a circular table without restrictions? (Two seatings are considered the same if one is a rotation of the other.)
There are 10 people to place, so we can place them in 10! ways, but this counts each arrangment 10 times (once for each rotation of the same arrangement). So the number of ways to seat them is 10!/10 = 9! = 362,880.