#ATTENDANCE QUIZ FOR LECTURE 13 of Dr. Z.'s Math454(02) Rutgers University


# Please Edit this .txt page with Answers


#Email  ShaloshBEkhad@gmail.com 
#Subject: p13
#with an attachment called
#p13FirstLast.txt
#(e.g. p13DoronZeilberger.txt)


#Right after finishing watching the lecture but no later than Oct. 20, 2020, 8:00pm




THE NUMBER OF ATTENDANCE QUESTIONS WERE:


PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH BY THE ANSWER


1. Describe the problem that Euler solved regarding 7 bridges. 


A: The object of the problem was to devise a walk through the city of Prussia that involved crossing each out of 7 bridges only once. 


2. If you toss a fair coin 2000 times what is the probability that you get 1000 heads and tails. 


A: 0.01784


3. If you roll a fair die 6000 times what is the probability that each of the outcomes occurs exactly 1000 times? 


A: (⅙)^6000


4. Pick 5 random Facebook friends. For each of them pick 3 friends. For each of the friends of friends pick 3 friends. Label the people picked 1, 2, …, n. 


A: RandDG(5,12) 


5. Look at the cities that border Piscataway. And for each of them that border them and again until you get to Princeton. (i) Construct the graph and (ii) find the number of paths from Piscataway to Princeton. 


1. Find the actual set using paths (and list them)
2. By using NuPaths
3. By using GFt 


(i) RandDG(2,2) 
(ii) Nops(Paths(G,2,2) 


1. Paths(G,2,2) 
2. NuPaths([{1,2},{2,3},{3,4},{1,2}],2);
3. GFt([{1,2},{2,3},{3,4},{1,2}],2,t)