Talk show host Ralph Burke has exactly one guest on his show each day,

Question

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

pr3mk5 · Answer

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'.

EgmatQuantExpert · Answer

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 
• Hence, the total number of possible different schedules = 5 * 4 * 3 * 6 * 10 = 3600

As per the options, the correct answer is option C.

Answer: C

ScottTargetTestPrep · Answer

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.

Answer: C

push12345 · Answer

Choosing two politicians = 5C2
But politicians have two ways ,so 2 selected ones have two cases to appear on different day
So total case for politicians= 2*5C2

Actor= 3C1

Athelete= 6C1

Remaining = 3 politicians + 2 actor + 5 athelete=10
Out of these one on Friday so = 10C1

Total= 2*5C2*3C1*6C1*10C1= 3600

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Talk show host Ralph Burke has exactly one guest on his show each day,

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