Inclusion-Exclusion Principle



Could someone explain to me how to use the Inclusion-Exclusion
Principle to solve this problem.

Question: A carousel has eight seats, each seat is distinct. Eight
girls are seated on the carousel facing forward ( each girl looks at
another girl's back). In how many ways can they change seats so that
each has a different girl in front of her? How can the problem change
when the seats are identical?

Thanks a lot for the help.

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