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  3. combinatorics 30 points total a a prospective student is planning...

Question: combinatorics 30 points total a a prospective student is planning...

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Combinatorics. (30 points total) a) A prospective student is planning to visit several universities during the application process. She decides to visit the University of Rochester, Cornell University, Standford University, MIT, and Johns Hopkins University. How many different itineraries can she arrange for flights to visit all of these universities in one long trip? (For example: University of Rochester Cornell UniversityStandford UniversityMITJohns Hopkins University) Note that rearranging the order of the cities you visit will result in a different itinerary regardless of how the cities are rearranged. b) Suppose the prospective student in part (a) can only visit three universities. How many different itineraries can she choose from now? c) A U of R student is selecting courses for the Fall 2019 semester. She decides to choose from a total of 28 courses. How many different ways can she register for classes if she intends to register for a total of 4 courses? (Hint: Is there a difference between registering for PHY141/PHL110/CSC161/ENG206A and ENG206A/PHY141/PHL110/CSC1617) d) The U of R student described in part (c) just learned that 4 of the courses were cancelled, and the professor of a fifth is retiring after this semester. She decides that she will take the course given by the retiring professer in order to not risk the courses availability in the future. How many different ways can she register for classes now?

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