Project 1: Counting Methods

For this assignment, you can just upload this document with your answers provided after each question below.




If you worked with a partner, include their name



Please print and sign the honor pledge somewhere on the document



For this project, you should not use built-in functions or itertools.




A student is registering for classes for next semester. The courses she can enroll in are calculus, physics, organic chemistry, history, literature, French, and astronomy. She has room for four classes in her schedule, at the following times: 9am, 10am, 11am, 12pm. She wants to count all the possible versions of her schedule. Additionally, the student’s mother is helping her buy textbooks for her classes. Each course listed above has a specific textbook that is required with it. Therefore, a book order for the student will consist of four textbooks. Book orders are automatically listed in alphabetical order by the class subject (e.g., one book order could be astronomy, French, organic chemistry, physics). The student’s mother wants to count all the possible book orders that she could be making.



Make the beginnings of a carefully ordered list of all possible book orders. (Your list should include enough outcomes so that someone else can see and continue the pattern.)



Now make the beginnings of a carefully ordered list of all the possible versions of the student’s schedule, assuming she can’t register one class for multiple slots. (Your list should include enough outcomes so that someone else can see and continue the pattern.)



Here is a program written in Python. Does this count the possible book orders, schedules, or neither? Explain by referencing specific pieces of the provided code.
  


















































Write a program using for loops that lists AND counts all the possible book orders. Paste your code below. What are the first 20 outcomes that your program lists? What is the total number of outcomes? Hint: consider using < or <= instead of !=. (The logic and code for this problem and in problems 2 & 3 should closely resemble
the logic and code provided in problem 1c.)

 An 8-digit password is required to have three 0’s and five 1’s. You will determine how many unique passwords are possible.



First consider how you might notate possible outcomes in the process of listing them. For example, any of the following can represent the same outcome:




01011101




137 (the digits are the locations of the 0’s)




24568 (the digits are the locations of the 1’s)




Write a program that lists and counts the unique passwords. Provide your code, all outcomes, and the count.
















An 8-digit password is required to have exactly three 0’s. The other 5 digits can be any number 1-7, but numbers 1-7 may not be repeated.



Consider different options for notating possible outcomes. (Hint: it may be easier to think of a way to notate the location of the 0’s, rather than just writing the outcomes as a list of 8 digits) Then make a list of at least 20 possible passwords. (List the outcomes in an ordered, intentional way so as not to miss any if you kept going.)



Write a program that lists all the possible outcomes. Provide your code and the first 100 outcomes.



Suppose you have a password with m digits required to have exactly n 0’s. The other (m-n) digits can be any number 1-9 but numbers 1-9 may not be repeated. How many unique passwords exist? (Your answer should be in terms of m and n.)















A 5-letter password is to be constructed from the following letters: A, B, C, D, and E and the password must contain exactly 3 of the letters. (Obviously at least one of them will need to be used more than once to create a 5-letter password.)



Suppose A,B, and C are the letters selected and we use A twice, B twice, and C once. How many different passwords exist in this scenario?



Suppose A,B, and C are the letters selected and there are no other restrictions. How many different passwords exist in this scenario?



Now suppose we don’t put any restrictions on the letters chosen. (It could be A,B, and C, or it could be A, C, and D, or it could be B, D, and E, etc.) How many different passwords exist in this scenario?



You may solve problem 4 however you wish (with or without a program). If you write a program, you should clearly explain what each section of your code accomplishes. If you don’t use a program, you should show all your work and justify each computation.