A Senate committee has 5 Democrats and 5 Republicans. In how many distinguishable ways can they sit around a circular table if all the members of each party all sit next to each other?.
Answer: Choose any 5 consecutive seats in which to place the Democrats -- it doesn't matter which 5 consecutive seats that we choose, since we can rotate the table. Then there are ways to place the Democrats in their seats, and ways to place the Republicans in their seats, for a total of 14,400 arrangements.
That answer is the absoute correct answer from AOPS.