A Senate committee has 5 Democrats and 5 Republicans. In how many ways can they sit around a circular table if each member sits next to two members of the other party? (Two seatings are the same if one is a rotation of the other.)
+128460 "Anchor" a member of either party in one seat....for convenience, choose a Democrat to occupy this seat....we have 5 choices
Going counter-clockwise, we have 5 ways of choosing a member of the opposite party to sit to the right of the first person, 4 ways to choose the person to sit to the right of the second person, and so on
So.....the total ways =
D * R D R D R D R D R
5* 5 * 4 * 4 * 3 * 3 * 2 * 2 * 1 * 1 = 25 * 16 * 9 * 4 = 14400 ways
