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.)

Guest Mar 11, 2021

#1**+1 **

"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

CPhill Mar 11, 2021