Organizing Schedules (GRE problem)

Discrete Mathematics Level pending

Talk show host Ralph has exactly one guest on his show each day, and Ralph's show airs every Monday through Friday. Ralph always schedules politicians on Mondays and Wednesdays, actors on Tuesdays and athletes on Thursdays, but can have a guest of any one of these three kinds on Friday. No guest appears more than once per week on Ralph's show. If Ralph has five politicians, three actors and six athletes he could invite, and if no politician is also an actor or an athlete and no actor is also an athlete, how many different schedules of guests from Monday to Friday could Ralph create?

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