Question

python

11.8 Multiple committees The eventual goal of this assignment is to compute the total number of ways of forming a collection of committees from an academic department of n professors. The first task is to write a function called committee to compute the number of ways of forming a single committee with members from a collection of n people. This is the same as compușing the number of ways of choosing r people out of n to sit at the first of two tables, and is therefore nl / (ri"(n-1)) by the reasoning given in the zyLab in section 6.18 on seating a large group at multiple tables. Make sure the function returns an integer, not a floating point number with a decimal point. In addition to the fact that this must now be a function, there there are now some further enhancements. First of all, there is the potential that the committee might need a chairperson. If so, there are r choices for the chairperson for each of the possible ways of selecting the committee membership, so there are r*(n)/(ri*(n-1)) - n!/((-1)}"(n-1)) ways of forming such a chaired committee. Another way of thinking how to form such a committee is to choose the chairperson first (there are n possible choices for that). and then for each possible chairperson, choose the remaining r1 members out of the remaining n-1 people there are (n-1)!/((-1)((n-1)- (P-1))) ways of doing that). So the total number of ways is n*(n-1)/((r-1)!*((n-1)-(1-1)). Since n*(n-1) = nland (n-1)-(-1) = nr. this gives the same final formula n!/((-1)(n-1)). Your function definition must be of a form like def committee (people, members, chairperson) : where the parameter people is an integer giving the number of people to choose from (called 'n' in the formulas above), the parameter members is an integer giving the number of members in the committee (called 'r' in the formulas above) and the parameter "chairperson is a boolean variable which is true if a chairperson is required, and the formula in the fourth paragraph of this specification must be used and False if the committee has no chairperson, and the formula in the second paragraph must be used. You must use exactly these names for the parameters, because your function will be be called by keyword arguments using these parameter names in some of the tests, instead of just relying on the parameter order. Write your function in a file named committee.py, and upload it to zyBooks for the first few tests, which will exercise as it as a module using programs already at zyBooks that import your committee function from it. (1) The first test is with the following calls:

Answer 1

Answer:

1)

def factorial(n):
if n==0:
return 1
else:
return n*factorial(n-1)
def committee(people,members,chairperson):
if(chairperson):
return (factorial(people)//(factorial(members-1)*factorial(people-members)))
else:
return (factorial(people)//(factorial(members)*factorial(people-members)))
  
print(committee(10, 3, True))
print(committee(10, 3, False))
print(committee(members = 3, people = 10, chairperson = True))
print(committee(chairperson = False, members = 3, people = 10))
print(committee(2, 2, True))
print(committee(3, 3, False))

Output:

368 128 368

2)

def factorial(n):
if n<0:
raise ValueError("Cannot take the factorial of a negative number")
if n==0:
return 1
else:
return n*factorial(n-1)
  
def committee(people,members,chairperson=True):
if people<=0:
raise ValueError("People count must be positive.")
if members>people:
raise ValueError("Member count must not be greater than people count.")
if(chairperson):
return (factorial(people)//(factorial(members-1)*factorial(people-members)))
else:
return (factorial(people)//(factorial(members)*factorial(people-members)))
  

print(committee(10, 3))
print(committee(members = 3, people = 10))
print(committee(2, 2))

Output:

368 368

3,4,5)

committee.py:

def factorial(n):
if n<0:
raise ValueError("Cannot take the factorial of a negative number")
if n==0:
return 1
else:
return n*factorial(n-1)
  
def committee(people,members,chairperson=True):
if people<=0:
raise ValueError("People count must be positive.")
if members>people:
raise ValueError("Member count must not be greater than people count.")
if(chairperson):
return (factorial(people)//(factorial(members-1)*factorial(people-members)))
else:
return (factorial(people)//(factorial(members)*factorial(people-members)))

multiple_committees.py

from committee import committee
professors=int(input("Enter the number of professors in the department:"))
canProfessorOnMultipleCommittee=input("Can a professor be on multiple committees? Enter y or n:")
TotalNoOfWays=1

while(True):
committeeName=input("Enter that name of the committee:")
if(not committeeName):
break
needChairPerson=input("Does the committee need a chairperson? Enter y or n:")
members=int(input("Enter the number of members:"))
if(professors<members and professors>0):
print("Assigning only ",professors,"members to the ",committeeName," committee.")
print("There are ",professors," ways to form the ",committeeName," committee.")
TotalNoOfWays*=professors
break
try:
if(needChairPerson=='n'):   
noOfWays=committee(professors,members,False)
else:
noOfWays=committee(professors,members)
TotalNoOfWays*=noOfWays
print("There are ",noOfWays," ways to form the ",committeeName," committee.")
if(canProfessorOnMultipleCommittee=='n'):
professors=professors-members
except ValueError as e:
print(e)
print("There are ",TotalNoOfWays," ways to form all the committees.")   

SCREENSHOTS OF THE CODE SHOWN BELOW:

1 #committee.py 2 def factorial(n): if n<: raise ValueError("Cannot take the factorial of a negative number") if n==0: return 1 else: о л ьш мно о со о л ьш return n'factorial(n-1) def committee (people, members, chairperson=True): if people<=6: raise ValueError("People count must be positive.") if members >people: raise ValueError("Member count must not be greater than people count.") if(chairperson): return (factorial (people) //(factorial (members-1)*factorial(people-members ))) else: return (factorial (people)//(factorial(members) *factorial (people-members))) о со

20 #multiple_commitees.py 21 #from committee import committee 22 professors=input("Enter the number of professors in the department:") 23 canProfessorOnMultipleCommittee=input("Can a professor be on multiple committees? Enter y or n:") 24 TotalNoofways=1 while(True): committeeName=input("Enter that name of the committee:") if(not committeeName): break needChairperson=input("Does the committee need a chairperson? Enter y or n:") members=input("Enter the number of members:") if(professors<members): print("Assigning only ", professors,"members to the ", committeeName," committee.") break if(needChairperson=='n') noofways=committee (professors, members, False) else noofways=committee (professors, members) TotalNoofways*=noof Ways print("There are ", noofways," ways to form the ", committeeName," committee."") if(canProfessorOnMultipleCommittee=='n'): professors=professors-members except ValueError as e: print(e) print("There are ", TotalNoofways," ways to form all the committees.")

Output:

Enter the number of professors in the department:12 Can a professor be on multiple committees? Enter y or niy Enter that name of the committee: Admissions Does the committee need a chairperson? Enter y or niy Enter the number of members:4 There are 1980 ways to form the Admissions Committee. Enter that name of the committee: Petitions Does the committee need a chairperson? Enter y or nin Enter the number of members:2 There are 66 ways to form the Petitions Committee. Enter that name of the committee: Student Welfare Does the committee need a chairperson? Enter y or n:n Enter the number of members: 4 There are 495 ways to form the Student Welfare committee. Enter that name of the committee: There are 64686600 ways to form all the committees.

Enter the number of professors in the department: -2 Can a professor be on multiple committees? Enter y or n:n Enter that name of the committee: Compensation Does the committee need a chairperson? Enter y or nin Enter the number of members:-2 People count must be positive. Enter that name of the committee: There are 1 Ways to form all the committees. ELELALE CUPPOGOEND. I utbe. .1- comuto

Enter the number of professors in the department:5 Can a professor be on multiple committees? Enter y or n:n Enter that name of the committee:Compensation Does the committee need a chairperson? Enter y or ny Enter the number of members:-3 Cannot take the factorial of a negative number Enter that name of the committee: Compensation Does the committee need a chairperson? Enter y or niy Enter the number of members:3 There are 30 ways to form the Compensation Committee. Enter that name of the committee: Graduate Admissions Does the committee need a chairperson? Enter y or niy Enter the number of members:3 Assigning only 2 members to the Graduate Admissions Committee. There are 2 ways to form the Graduate Admissions Committee. There are 60 ways to form all the committees.

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