[administration]

Q. Six people A through f sit around a circular table. A and B sit together. C and D do not sit together. In how many ways they can sit?

[Wonder Boy]

For Circular permutation : The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is (n-1)!

 

Now since A,B sit together, so considering them as 1 unit.

The no. of ways in which they can sit (leaving C & D condition) = (5-1)! x 2 = 48. (since A,B can interchange places among them and form new arrangement so we multiply by 2)

Now We will find the no. of ways in which both A,B and C,D sit together.

= (4-1)! x 2 x 2 = 24.

Hence required no. of ways in which A,B sit together and C,D do not sit together = 48-24 = 24 Ans.

[Author]

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