- #1
Shahed al mamun
- 5
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6 people are invited to a dinner party and they are sitting on a round table.
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.
Can this problem be solved with inclusion-exclusion principle ? If so can anyone give me intuitive explanation of the solution process.
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.