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Monday through Friday. Burke 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 Burke’s show. If Burke 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 Burke create?

Monday through Friday. Burke 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 Burke’s show. If Burke 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 Burke create?

A) 30

B) 1,200

C) 3,600

D) 4,500

E) 6,300

Take the task of creating the schedules and break it into stages.

Stage 1: Select Monday's guest This must be a politician. There are 5 politicians to choose from, so we can complete stage 1 in 5 ways

Stage 2: Select Tuesday's guest This must be an actor. There are 3 actors to choose from, so we can complete stage 2 in 3 ways

Stage 3: Select Wednesday's guest This must be a politician. Since we already selected a politician during state one, there are now 4 politicians remaining to choose from. So we can complete stage 3 in 4 ways

Stage 4: Select Thursday's guest This must be an athlete. There are 6 athletes to choose from, so we can complete stage 4 in 6 ways

Stage 5: Select Friday's guest There WERE 14 guests to begin with (5 + 3 + 6 = 14). However, in the first 4 stages, we have scheduled 4 of those guests. So, there are now 10 guests remaining to choose from So we can complete stage 5 in 10 ways

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus schedule all 5 days) in (5)(3)(4)(6)(10) ways (= 3600 ways)