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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?
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)
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
On Monday there are 5 options, Tuesday 3 options, Wednesday 4 options, Thursday 6 options, and Friday 10 options (since he can select from 3 politicians, 2 actors, and 5 athletes).
So the total number of options for the week is 5 x 3 x 4 x 6 x 10 = 3,600.
Re: Talk show host Ralph Burke has exactly one guest on his sho
[#permalink]
14 Dec 2018, 09:45
I didn't think it would be that simple, was the question trying to lead us by giving us the extraneous information "if no politician is also an actor or an athlete and no actor is also an athlete?"
Why does that not change the number of people for Friday, since it seems that there is an overlap in our set of people?
Re: Talk show host Ralph Burke has exactly one guest on his sho
[#permalink]
14 Dec 2018, 15:23
1
Expert Reply
QuantumWonder wrote:
I didn't think it would be that simple, was the question trying to lead us by giving us the extraneous information "if no politician is also an actor or an athlete and no actor is also an athlete?"
Why does that not change the number of people for Friday, since it seems that there is an overlap in our set of people?
Hi..
the information is required "if no politician is also an actor or an athlete and no actor is also an athlete?" Had there been an overlap, the answer would have become more complex.
There are 2 different days for politician so any one of 5 goes on Monday, any one of the remaining 4 on wednesday - so 5*4 There is 1 different day for actor, so any of 3 goes on Tuesday - so 3 There is 1 different day for athlete, so any of 6 goes on Thursday - so 6 Now any of the remaining of above can be called on friday so any one of remaining (3+2+5)=10
Re: Talk show host Ralph Burke has exactly one guest on his sho
[#permalink]
15 Dec 2018, 17:25
chetan2u wrote:
QuantumWonder wrote:
I didn't think it would be that simple, was the question trying to lead us by giving us the extraneous information "if no politician is also an actor or an athlete and no actor is also an athlete?"
Why does that not change the number of people for Friday, since it seems that there is an overlap in our set of people?
Hi..
the information is required "if no politician is also an actor or an athlete and no actor is also an athlete?" Had there been an overlap, the answer would have become more complex.
There are 2 different days for politician so any one of 5 goes on Monday, any one of the remaining 4 on wednesday - so 5*4 There is 1 different day for actor, so any of 3 goes on Tuesday - so 3 There is 1 different day for athlete, so any of 6 goes on Thursday - so 6 Now any of the remaining of above can be called on friday so any one of remaining (3+2+5)=10
hence answer - 5*4*3*6*10=3600
I see, I think I didn't read very carefully and didn't notice they were implying it was a mutually exclusive set. This definitely allows us to solve more easily.
Re: Talk show host Ralph Burke has exactly one guest on his sho
[#permalink]
29 Nov 2023, 13:38
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