Problem 5. (20 pts) Two parents go with their three kids to the theatre, and they have tickets for five consecutive seats. (a) To avoid any chance of fraternal bickering, the parents decide that the kids cannot sit next to each other. How many different ways can the family sit together according to this rule if they seat along five consecutive seats? (b) Now, we allow kids to sit next to each. How many ways would there be if the only rule was that the two parents want to sit together?
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