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Bunuel
Franklin School of Business is organizing a weekend series for business students to learn from academic and business experts. The series will be in the form of interviews with experts and will take place on the first Saturday and Sunday of the spring semester. On both days, five speakers will be interviewed, each of them will either be a faculty or an entrepreneur. In alignment with the school’s pedagogy, the majority of interviews on one of the days will not be from Finance. On the other day, at least four entrepreneurs will be interviewed. Neither day will have more than two interviews with experts from the same industry.

Four experts on each day have already been confirmed. The following schedule shows the experts’ details – profession, area of expertise, and industry.

Saturday


O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail
Sunday


Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing
Select an expert who could be the fifth expert on either day. Then select an expert who could be the fifth expert on neither day. Make only two selections, one in each column.



­
 


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­On one of the day Finance should not be in majority.
On other day atleast 4 Entrepreneur interviews.
=> Other day than the day on which Finance is in minority should have atleast 4 Entrepreneur interviews.

Now, on Sunday as only 2 Entreprenuers are there we can not have at least Entrepreneur interviews despite of assigning 5th interviewer.
So, we have to complete 4 Entrepreneur interviews on Saturday and Sunday must not have majority Finance interviews.

1st column: 5th interviewer who can be on either of the day.
Mulick: Entrepreneur, HR, Automobiles
This interviewer is not an expert in Finance and is an expert in Entreprenuer means we can assign on either day without violating rules.

2nd column: 5th interviewer who can be on neither of the day.
Crowe: Faculty, Finance, Sports
This interviewer must have experties in Finance but not in Entreprenuer so that we can not assign on either of the day to follow the rules.

Rest all can be assigned to at least one of the days.
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Bunuel
Franklin School of Business is organizing a weekend series for business students to learn from academic and business experts. The series will be in the form of interviews with experts and will take place on the first Saturday and Sunday of the spring semester. On both days, five speakers will be interviewed, each of them will either be a faculty or an entrepreneur. In alignment with the school’s pedagogy, the majority of interviews on one of the days will not be from Finance. On the other day, at least four entrepreneurs will be interviewed. Neither day will have more than two interviews with experts from the same industry.

Four experts on each day have already been confirmed. The following schedule shows the experts’ details – profession, area of expertise, and industry.

Saturday


O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail
Sunday


Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing
Select an expert who could be the fifth expert on either day. Then select an expert who could be the fifth expert on neither day. Make only two selections, one in each column.



­
 


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­As given:
1. One of the days can't have finance as majority while other day has to have entrepreneur as majority
2. Neither day will have more than two interviews with experts from the same industry.

For Saturday:
1. We have to have an entrepreneur ; 2. We can't have ecommerce as industry

For Sunday:
1. We can't have Finance; 2. We can't have Retail

So to select an expert for either days, we should have an Entrepreneur; not in finance, retail or ecommerce. So Mulick (Entrepreneur, HR, Automobiles) Satisfys
To select an expert for neither day; we can have a combo of not entrepreneur; in Finance; in retail or ecommerce. So Crowne (Faculty, Finance, Sports) satisfys
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Because at least four entrepreneurs will be interviewed on one day, it has to be Saturday, because there are already 3. 
Then fifth expert on either day has to be entrepreneur. 

Taffe: Entrepreneur, Finance, Sports
Pyne: Entrepreneur, Marketing, E-commerce
Mulick: Entrepreneur, HR, Automobiles

Since the majority of interviews on one of the days will not be from Finance, it cannot be Taffe. 
Since neither day will have more than two interviews with experts from the same industry, it cannot be Pyne. 

Therefore, the answer is Mulick for fifth expert on either day

Then fifth expert on neither day has to be faculty. 
Crowe: Faculty, Finance, Sports
Garbo: Faculty, Strategy, Hospitality
Vandaley: Faculty, Marketing, E-commerce

Since the majority of interviews on one of the days will not be from Finance, picking Crowe will be good for neither day as it will break for one of the days. 

Therefore, the answer is Crowe for fifth expert on neither day








 ­
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Bunuel
Franklin School of Business is organizing a weekend series for business students to learn from academic and business experts. The series will be in the form of interviews with experts and will take place on the first Saturday and Sunday of the spring semester. On both days, five speakers will be interviewed, each of them will either be a faculty or an entrepreneur. In alignment with the school’s pedagogy, the majority of interviews on one of the days will not be from Finance. On the other day, at least four entrepreneurs will be interviewed. Neither day will have more than two interviews with experts from the same industry.

Four experts on each day have already been confirmed. The following schedule shows the experts’ details – profession, area of expertise, and industry.

Saturday

O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail
Sunday

Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing
Select an expert who could be the fifth expert on either day. Then select an expert who could be the fifth expert on neither day. Make only two selections, one in each column.
 
Taffe can be on Saturday due to Entrepreneur but cannot be on Sunday due to Finance.
Crowe cannot be on Saturday due to not being an Entrepreneur and also cannot be on Sunday due to Finance -- Neither 
Pyne cannot be on Saturday due to more than 2 E-commerce and can be on Sunday since there is no clash.
Mulick Can be on both days since there is no clash -- Either
Garbo cannot be on Saturday and can be on Sunday
Vandaley cannot be on Saturday due to more than 2 E-commerce and can be on Sunday since no clash­
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The hard rules which were restrictive are: 
Saturday - Should be entrepreneur. Should not be E-commerce. 
Sunday - Should not be Finance. Should not be Retail. 
So, the options left are Mulick: Entrepreneur, HR, Automobiles - for either day. 
Crowe: Faculty, Finance, Sports for neither day because Entrepreneur is necessary for Saturday and Finance can't be the subject of more than 2 interviews on Sunday. 
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Quote:
­Franklin School of Business is organizing a weekend series for business students to learn from academic and business experts. The series will be in the form of interviews with experts and will take place on the first Saturday and Sunday of the spring semester. On both days, five speakers will be interviewed, each of them will either be a faculty or an entrepreneur. In alignment with the school’s pedagogy, the majority of interviews on one of the days will not be from Finance. On the other day, at least four entrepreneurs will be interviewed. Neither day will have more than two interviews with experts from the same industry.

Four experts on each day have already been confirmed. The following schedule shows the experts’ details – profession, area of expertise, and industry.

Saturday

O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail

Sunday

Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing

Select an expert who could be the fifth expert on either day. Then select an expert who could be the fifth expert on neither day. Make only two selections, one in each column.
Either day: Mulick: Entrepreneur, HR, Automobiles, since we need 4 entreprenuers on atleast one day, this can take up Saturday, also the area is different from all, meaning it won't affect Finance majority on either day.

Neither day: Crowe: Faculty, Finance, Sports, since we can't have more than 2 same areas, we can't have any finance guy on either day.
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Franklin School of Business is organizing a weekend series for business students to learn from academic and business experts. The series will be in the form of interviews with experts and will take place on the first Saturday and Sunday of the spring semester. On both days, five speakers will be interviewed, each of them will either be a faculty or an entrepreneur. In alignment with the school’s pedagogy, the majority of interviews on one of the days will not be from Finance. On the other day, at least four entrepreneurs will be interviewed. Neither day will have more than two interviews with experts from the same industry.

Four experts on each day have already been confirmed. The following schedule shows the experts’ details – profession, area of expertise, and industry.

Saturday
O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail

Sunday
Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing

Select an expert who could be the fifth expert on either day. Then select an expert who could be the fifth expert on neither day. Make only two selections, one in each column.





Solution: Given conditions are:
  • One of the days should not have a majority of interviews from Finance. This means no more than two Finance experts on that day.
  • One of the days should have at least four entrepreneurs.
  • Neither day should have more than two experts from the same industry.

Confirmed experts on Saturday
  • O’Reilly: Faculty, Finance, Fashion
  • Hoffman: Entrepreneur, Marketing, E-commerce
  • Epstein: Entrepreneur, Marketing, E-commerce
  • Jenson: Entrepreneur, Finance, Retail

Findings:
  1. There are already 2 Finance experts (O’Reilly, Jenson).
  2. There are already 2 experts from the E-commerce industry (Hoffman, Epstein).
  3. To ensure no majority in Finance, the fifth expert should not be from Finance.
  4. To ensure no more than two experts from the same industry on one day, the fifth expert should not be from E-commerce.
  5. The fifth expert must be an Entrepreneur to have at least four entrepreneurs.

Candidates who are entrepreneurs: Taffe, Pyne, and Mullick 
Due to finding 4,
Possible candidates: Mullick, Taffe
Candidates not feasible: Pyne, Crowe, Garbo, Vandaley


Confirmed experts on Sunday
  • Martinez: Entrepreneur, Finance, Retail
  • Kahl: Entrepreneur, Finance, Retail
  • Wahba: Faculty, Strategy, Education
  • Emanuel: Faculty, Operations, Manufacturing

Findings:
  1. There are already 2 Finance experts (Martinez, Kahl).
  2. There are already 2 experts from the Retail industry (Martinez, Kahl).
  3. To ensure no majority in Finance, the fifth expert should not be from Finance.
  4. To ensure no more than two experts from the same industry on one day, the fifth expert should not be from Retail.
  5. The fifth expert can be either a Faculty or an Entrepreneur, as currently, there are 2 Entrepreneurs and 2 Faculty.

Due to findings 3 and 4
Possible candidates: Pyne, Mullick, Garbo, Vandaley
Candidates not feasible: Taffe, Crowe

Since the condition of interviewing 4 entrepreneurs on a day can only be me on Saturday (while the condition of interviewing no more than 2 Finance experts on a day can be violated), the condition of interviewing no more than 2 Finance experts has to be met on Sunday.

Based on the above conclusion and the findings from both days,
The expert who can be picked for either day = Mullick
The expert who can be picked for neither day = Crowe
­
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­From the statement given, we can gauge that Sunday is the day that majority will not be from the finance category and Saturday where at least 4 participants will be entrepreneurs.

Therefore, we can arrive at the conclusion that in Saturday, the additional Paterson has to be an Entrepreneur and not from E-commerce as there already two of them selected.

In Sunday, the person selected should not be from Finance and should not be from the Retail category as well. 

Keeping these conditions in mind, 

Either day - Option D

Neither day - Option B
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According to the Conditions given,

We can easily deduce that for either day- Mulick: Entrepreneur, HR, Automobiles is our option

And for Neither day- Crowe: Faculty, Finance, Sports is our option
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Answer: Either day: Mulick; Neither day: Crowe.

Conditions given: 1 day has to have 4 entrepreneurs, the other day will not have a majority of Finance. No 3 people of same industry.

Saturday |  Sunday 
F, Fin, F  |  E, Fin, R
E, Mar, E |  E, Fin, R
E, Mar, E |  F, Str, E
E, Fin, R |  F, Ops, M

So comparing this with the conditions given, we can have only an entrepreneur for Saturday (4 entrepreneurs) and thus Sunday will not have a majority of Finance, thus sunday can't have finance.

Now we check options:
  • Taffe: Entrepreneur, Finance, Sports
Can be on Saturday, can't be on Sunday (finance)
  • Crowe: Faculty, Finance, Sports
Can't be on Saturday (no entrepreneur), Can't be on Sunday (Finance)
  • Pyne: Entrepreneur, Marketing, E-commerce
Can't be on Saturday (E-Commerce), Can be on Sunday
  • Mulick: Entrepreneur, HR, Automobiles
Can be on Saturday, Can be on Sunday
  • Garbo: Faculty, Strategy, Hospitality
Can't be on Saturday (not entrepreneur), Can be on Sunday
  • Vandaley: Faculty, Marketing, E-commerce
Can't be on Saturday (not entrepreneur, E-commerce), Can be on Sunday­
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Rule 1: the majority of interviews on one of the days will not be from Finance
Rule 2: On the other day, at least four entrepreneurs will be interviewed
Rule 3: no more than two interviews with experts from the same industry.
­
Saturday

O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail

Sunday

Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing

Taffe: Cannot be either, only 1 day, breaks Rule 1
Crowe: neither day, breaks Rule 1 and Rule 2
Pyne: Breaks Rule 3 on Saturday
Mulick: Can be either day, breaks no rule on both sides
Garbo: Breaks Rule 2, Entrepreneur needed
Vandaley: Breaks Rule 2, Entrepreneur needed
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Day A: at least 4 entrepreneurs will be interviewed.
Day B: no more than 2 from Finance. 
Neither day will have more than two interviews with experts from the same industry.

---

Sat: 3 Entrepreneur, 1 Falculty
Sun: 2 Entrepreneur, 2 Falculty
=> Sat must be Day A
=> Sun is Day B

Sun already has 2 Finance
=> For B: The 5th cannot be Finance

Sat: 2 E-Com
Sun: 2 Retail
=> The 5th cannot be E-Com (A) and Retail (B)

So the rẻquirement for the 5th:
     Profession               Experitise           Industry   
A   Entrepreneur                                    x E-Com
B                                x Finance            x Retail

-------------------------------------

Taffe: Entrepreneur, Finance, Sports
=> Can be A, but not B

Crowe: Faculty, Finance, Sports
=> Cannot be either A or B

Pyne: Entrepreneur, Marketing, E-commerce
=> Can be B but not A 

Mulick: Entrepreneur, HR, Automobiles
=> Can be A or B

Garbo: Faculty, Strategy, Hospitality
=> Can be B but not A

Vandaley: Faculty, Marketing, E-commerce
=> Can be B but not A


Either: Mulick
Neither: Crowe


 
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­Let's look at question stem,
We are given:
1. Five speakers will be interviewed, each of them will either be a faculty or an entrepreneur.
2. The majority of interviews on one of the days will not be from Finance.
3.  On the other day, at least four entrepreneurs will be interviewed.
4. Neither day will have more than two interviews with experts from the same industry.

And we are given following information about current speakers:
Saturday
O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail

Sunday
Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing

There are 3 Entrepreneurs on Saturday and 2 Entrepreneurs on Sunday. This means that on Saturday there will be 4 Entrepreneurs.
This implies that on Sunday, majority of interviews will not be from Finance. Majority means 3 in case of 5. So, there can be only 2 finance speakers on Sunday.
This gives us following information for what we should look for in 5th speaker.

Saturday - 
Profession must be Entrepreneur, Industry cannot be E-commerce (condition-4)

Sunday -
Area of expertise cannot be finance (already have 2), Industry cannot be Retail (condition-4)

We need to select an expert who could be the fifth expert on either day. Then select an expert who could be the fifth expert on neither day. 

Looking at the options:
A. Taffe: Entrepreneur, Finance, Sports
He can be speaker on Saturday but not on Sunday (Area of expertise is finance)
Eliminate

B. Crowe: Faculty, Finance, Sports
He cannot be speaker on Saturday (profession is not entrepreneur) and also cannot be speaker on Sunday (Area of expertise is finance)
Select for Neither day

C. Pyne: Entrepreneur, Marketing, E-commerce
He can be speaker on Sunday but not on Saturday (Industry cannot be E-commerce)
Eliminate

D. Mulick: Entrepreneur, HR, Automobiles
He can be speaker on Saturday and on Sunday too.
Select for both days

E. Garbo: Faculty, Strategy, Hospitality
He cannot be speaker on Saturday (profession is not entrepreneur) but he can be on Sunday
Eliminate

F. Vandaley: Faculty, Marketing, E-commerce 
He cannot be speaker on Saturday (profession is not entrepreneur and Industry cannot be E-commerce) but he can be on Sunday
Eliminate­
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Constraints:

Majority of interviews on one of the days will not be from Finance.
On the other day, at least four entrepreneurs will be interviewed.
Neither day will have more than two interviews with experts from the same industry.
Thus,
Either day: Garbo (Faculty, Strategy, Hospitality) - fits well as it avoids Finance and industry overlap.
Neither day: Crowe (Faculty, Finance, Sports) - since we need to avoid adding more Finance experts and also don't fit the entrepreneur criteria for Sunday.
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­Either day: Mulick: Entrepreneur, HR, Automobiles
Neither day: Garbo: Faculty, Strategy, Hospitality


Conditions: 

1. The majority of interviews on one of the days will not be from Finance
2. On the other day, at least four entrepreneurs will be interviewed
3. Neither day will have more than two interviews with experts from the same industry

Schedule for Saturday and Sunday

Saturday

O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail

Sunday

Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing

based on above we can infer that:

1. Condition 2 is met by Saturday's schedule
2. Condition 1 is met by Sunday's schedule

Case 1:
Either day


1. Entrepreneur can be on either day
2. E-commerce cannot be on a Saturday
3. Retail cannot be on a Sunday
4. Finance cannot be on Saturday (else Finance condition 1 will be met by Saturday's schedule as well)

Based on the above conditions only Choice 4 is the right candidate: Mulick: Entrepreneur, HR, Automobiles


Case 2:
Neither day


1. The combination of Retail and Finance cannot be on either days, as Conditions 1 and 3 will be violated
2. Entrepreneur is a must for Saturday's schedule => any profession other than Entrepreneur cannot be on Saturday
3. Any area of expertise other than Strategy and Operations can be on Sunday
4. The combination of E-commerce cannot be on Saturday, as Condition 3 will be violated

based on above conditions, we get :

Pyne: Entrepreneur, Marketing, E-commerce -> possible on Sunday
Garbo: Faculty, Strategy, Hospitality -> Cannot be on either
Vandaley: Faculty, Marketing, E-commerce -> possible on Sunday

Hence, the only matching choice is : Garbo: Faculty, Strategy, Hospitality
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Bunuel
Franklin School of Business is organizing a weekend series for business students to learn from academic and business experts. The series will be in the form of interviews with experts and will take place on the first Saturday and Sunday of the spring semester. On both days, five speakers will be interviewed, each of them will either be a faculty or an entrepreneur. In alignment with the school’s pedagogy, the majority of interviews on one of the days will not be from Finance. On the other day, at least four entrepreneurs will be interviewed. Neither day will have more than two interviews with experts from the same industry.

Four experts on each day have already been confirmed. The following schedule shows the experts’ details – profession, area of expertise, and industry.

Saturday

O’Reilly: Faculty, Finance, Fashion
Hoffman: Entrepreneur, Marketing, E-commerce
Epstein: Entrepreneur, Marketing, E-commerce
Jenson: Entrepreneur, Finance, Retail
Sunday

Martinez: Entrepreneur, Finance, Retail
Kahl: Entrepreneur, Finance, Retail
Wahba: Faculty, Strategy, Education
Emanuel: Faculty, Operations, Manufacturing
Select an expert who could be the fifth expert on either day. Then select an expert who could be the fifth expert on neither day. Make only two selections, one in each column.
Note the conditions first. One day say day 1 - Fin. will not be majority. Fin will be 1 or 2.
Other day, say day 2- atleast 4 entrepreneurs- Sat. is the Day 2 as on sunday there are only 2 entrepreneurs and there is room for only 1. 

Therefore, Saturday- 4 entrepreneurs, Sunday- max 2 finance. This tells us that an expert selected on Saturday will only be an entrepreneur and expert on sunday will not be from Finance.

The 3rd condition states that no more than 2 experts from same industry can be interviewed on each day. 

Analyze options:

Select an expert who could be the fifth expert on either day.-

On saturday, E-commerce expert will not be interviewed, Hence Pyne (P), Vandeley (V) will not be interviewed. (Vandeley is also a faculty and we need entrepreneur on Sat.) 
From entrepreneurs, it can either be Mulick (M) or Taffe (T) on Sat.
However, T cannot be the 5th expert on sunday otherwise Fin. will be a majority on sunday. Therefore, we can conclude that M can interview on either day.

Select an expert who could be the fifth expert on neither day.-

As we saw in the earlier analysis, T can be interviewed on Sat but not Sunday. Hence eliminated.
Checking frow Crow (C), C cannot be interviewed on Sat as he is a faculty and also on Sun, because he is a fin expert and adding him on Sun would mean majority fin. Hence, C will not be interviewed in any of the two days.



 
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Saturday: 
Atleast one more Entrepreneur is required as sunday have 2. further any one with e-commerce cannot be here.

sunday:

Anyone from finance cannot join. anyone with retail cannot join.

Mulick: Entrepreneur-reqd for saturday,
           HR- non finance so ok for sunday
           automobile- satisfy both days.

Hence Mulick on either days

Crowe: Faculty- cannot join satuday
           finance- cannot join sunday

Hence crowe cannot be on either days

Ans: Mulick & Crowe­
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