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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.)

 Mar 11, 2021
 #1
avatar+118069 
+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

 

 

cool cool cool

 Mar 11, 2021
 #2
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Sorry CPhill, but your answer is wrong.

 Mar 11, 2021
 #3
avatar+118069 
0

Not good at this counting stuff.....maybe someone else has the correct answer   !!!!

 

 

 

cool cool cool

CPhill  Mar 11, 2021

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