- #1

- 5

- 0

Each person is sitting on a chair there are exactly 6 chairs.

So each person has exactly two neighboring chairs, one on the left and the other on the right.

The host decides to shuffle the sitting arrangements.

A person will be happy with the new arrangement if he can sit on his initial chair or any of his initial neighboring chairs.

- We have to find the number of different arrangements such that only 1 person is happy.
- We have to find the number of different arrangements such that only 2 persons are happy.

- We have to find the number of different arrangements such that only 3 persons are happy.

Can this problem be solved with inclusion-exclusion principle ? If so can anyone give me intuitive explanation of the solution process.