Problem 3 (Medium): Counting Students are picking their schedules for next semester and need to figure out their NUPath requirements. The overall course counts for each of the attributes are as follows: Societies/Institutions 271 Interpreting Culture 243 Creative Expression 157 Difference/Diversity 182 Natural/Designed World 136 Ethical Reasoning 100 Formal/Quantitative Reasoning 50 Analyzing/Using Data 135 Two schedules are the same if they have the same courses. i. Sarah is planning to take four courses next semester. She is planning to take 2 Formal/Quantitati Reasoning courses. She needs Societies/Institutions, Interpreting Culture, Creative Expres- sion, and Difference/Diversity. Assuming no course counts for more than one NUPath re- quirement and that she wants to do as many NUPath requirements as possible. How many schedules can she build? ii. A course can have 1 or 2 predefined NUPath attributes. Rick is planning to take 4 courses. He wants to maximize the number of possible NUPath requirements he can complete this semester. Rick wants to know how many schedules he can build. How many cases does Rick need to consider to do so? iii. Sam needs to take 2 courses for their major. These two courses each have one of the following attributes: Formal/Quantitative Reasoning, Natural/Designed World, or Analyzing/Using Data. They want to maximize the other attributes for the two courses, but they don't want to take any Creative Expression courses if they take an Interpreting Culture course. Sam wants to know how many schedules they can build. How many cases does Sam need to consider to do so? Problem 3 (Medium): Counting Students are picking their schedules for next semester and need to figure out their NUPath requirements. The overall course counts for each of the attributes are as follows: Societies/Institutions 271 Interpreting Culture 243 Creative Expression 157 Difference/Diversity 182 Natural/Designed World 136 Ethical Reasoning 100 Formal/Quantitative Reasoning 50 Analyzing/Using Data 135 Two schedules are the same if they have the same courses. i. Sarah is planning to take four courses next semester. She is planning to take 2 Formal/Quantitati Reasoning courses. She needs Societies/Institutions, Interpreting Culture, Creative Expres- sion, and Difference/Diversity. Assuming no course counts for more than one NUPath re- quirement and that she wants to do as many NUPath requirements as possible. How many schedules can she build? ii. A course can have 1 or 2 predefined NUPath attributes. Rick is planning to take 4 courses. He wants to maximize the number of possible NUPath requirements he can complete this semester. Rick wants to know how many schedules he can build. How many cases does Rick need to consider to do so? iii. Sam needs to take 2 courses for their major. These two courses each have one of the following attributes: Formal/Quantitative Reasoning, Natural/Designed World, or Analyzing/Using Data. They want to maximize the other attributes for the two courses, but they don't want to take any Creative Expression courses if they take an Interpreting Culture course. Sam wants to know how many schedules they can build. How many cases does Sam need to consider to do so