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# Talk show host Ralph Burke has exactly one guest on his sho

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Talk show host Ralph Burke has exactly one guest on his sho [#permalink]  05 Jun 2017, 02:28
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Talk show host Ralph Burke has exactly one guest
on his show each day, and Burke’s show airs every

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
[Reveal] Spoiler: OA

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Re: Talk show host Ralph Burke has exactly one guest on his sho [#permalink]  06 Jun 2017, 15:54
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Carcass wrote:
Talk show host Ralph Burke has exactly one guest
on his show each day, and Burke’s show airs every

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)

[Reveal] Spoiler:
C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: Talk show host Ralph Burke has exactly one guest on his sho   [#permalink] 06 Jun 2017, 15:54
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