SOLUTION: 8 guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in whi

Algebra ->  Permutations -> SOLUTION: 8 guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in whi      Log On


   

Question 490536: 8 guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
8 guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is?
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Pick a side: 2 ways
Arrange the 2 on one side: 2! = 2
Arrange the 3 on the other side: 3! = 6
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Pick 2 from the remaining 3: 3C2 = 3 ways
Put them on the side with 2: 1 way
Put the remaining person on the side with 3: 1 way
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Total # of arrangements: 2*2*6*3*1*1 = 72
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Cheers,
Stan H.