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

BTGmoderatorDC 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

OA C

Source: Princeton Review

We have 5 politicians, 3 actors, and 6 athletes

The guest order would be as following:

Monday: Politicians => Any of the 5 politicians can be invited => Number of ways = 5;

Tuesday: Actors => Any of the 3 actors can be invited => Number of ways = 3;

Wednesday: Politicians => Any of the 4 remaining politicians can be invited => Number of ways = 4; (It is given that a guest cannot be repeated)

Thursday: Athletes => Any of the 6 athletes can be invited => Number of ways = 6;

Friday: Any guest => Any of the remaining 10 guests can be invited => Number of ways = 10; (There are a total of 5 + 3 + 6 = 14 probables and 4 of them are already invited, so the remaining probables = 14 – 4 = 10)

Total number of ways = 5*3*4*6*10 = 3600 ways

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC 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

On Monday there are 5 options (politicians), Tuesday 3 options (actors), Wednesday 4 options (politicians, but only 4 of them), Thursday 6 options (athletes), and Friday 10 options (since he can select from 3 politicians, 2 actors, and 5 athletes).

Thus, the total number of guest schedules for the week is 5 x 3 x 4 x 6 x 10 = 3,600.

Answer: C