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cs109_fall21_pset1.pdf - –1– Chris Piech CS 109 Problem Set...

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– 1 –Chris PiechCS 109Problem Set #1Problem Set #1For each problem, briefly explain/justify how you obtained your answer.Brief explanations ofyour answer are necessary to get full credit for a problem even if you have the correct numericalanswer. The explanations help us determine your understanding of the problem whether or notyou got the correct answer. Moreover, in the event of an incorrect answer, we can still try to giveyou partial credit based on the explanation you provide. It is fine for your answers to includesummations, products, factorials, exponentials, or combinations; you don’t need to calculate thoseall out to get a single numeric answer.Note: all assignment submissions will be made online through Gradescope. You can find informationon signing up to submit assignments though Gradescope on the class webpage. If you handwriteyour solutions, you are responsible for making sure that you can produceclearly legiblescansof them for submission. You may use any word processing software you like for writing up yoursolutions. On the CS109 webpage we provide a template file and tutorial for the LATEX system, ifyou’d like to use it.1Written problemsSubmit your solutions to these written problems as a single pdf file on Gradescope.0. In this problem we show an example of a great student answer. It will get full points becauseit was explained well. But there is a mistake. Your job is to find the mistake.Problem: You are running a web site that receives 8 hits (in a particular second of time).Your web site is powered by 5 computers, and each hit to your web site can be serviced byany one of the 5 computers you have, where each computer is capable of processing as many(or as few) requests as it is given. In how many distinct ways can the hits be serviced?Student answer: This problem can be solved using the divider method. You need to dividethe==8hits among theA=5computers. The number of ways of dividing is=+A-1A-1=8+5-15-1=114=330.Mistake: Because the hits are distinct as stated in the problem, we useA=instead of thedivider method, following the Step Rule of Counting. UsingA=, we get58=390625
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Term
Fall
Professor
NoProfessor
Tags
Probability theory, Randomness

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