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08 May 2018, 00:43
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (02:41) correct
26%
(03:23)
wrong
based on 151
sessions
History
Date
Time
Result
Not Attempted Yet
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
A) 30
B) 1,200
C) 3,600
D) 4,500
E) 6,300
08 May 2018, 01:02
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five politicians, three actors and six athletes.
Politicians on two days - 5*4(since no guest appear more than once)
Actors one day - 3
Athlete one day - 6
Therefore - 5*4*3*6 = 360 ways
and for the remaining one day it could be anyone of the remaining politician or athlete, or an actor.
which is 3+2+5 = 10.
Multiplying 360 * 10 - 3600 ways. Hence 'C'.
Politicians on two days - 5*4(since no guest appear more than once)
Actors one day - 3
Athlete one day - 6
Therefore - 5*4*3*6 = 360 ways
and for the remaining one day it could be anyone of the remaining politician or athlete, or an actor.
which is 3+2+5 = 10.
Multiplying 360 * 10 - 3600 ways. Hence 'C'.
08 May 2018, 04:21
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Solution
Given:
• One guest, among politician, actor, and athlete, needs to be invited every day from Monday to Friday
• Mondays and Wednesdays are scheduled for politicians
• Tuesdays are scheduled for actors
• Thursdays are scheduled for athletes
• No guest appears more than once in a week
• Total number of people available – 5 politicians, 3 actors, and 6 athletes
To find:
• Number of different schedules can be created
Approach and Working:
• We can approach the problem by finding out the possibilities on day-to-day basis
- o The guests for Mondays and Wednesdays can be selected in \(^5C_1\) = 5 and \(^4C_1\) = 4 ways respectively
- o The guest for Tuesday can be selected in \(^3C_1\) = 3 ways
- o The guest for Thursday can be selected in \(^6C_1\) = 6 ways
- o As already 4 persons are selected, for Friday number of persons left = (5 + 3 + 6 – 4) = 10 and therefore, the guest in Friday can be selected in \(^10C_1\) = 10 ways
As per the options, the correct answer is option C.
Answer: C
