#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

#Q1 Describe the problem that Euler solved regarding 7 bridges ( 5min (start))

	A: The problem was that in the city of Konigsberg, was there a possible way to cross all seeven bridges once in one path?

#Q2 Draw it on a piece of paper with a line segement representing every edge (15min)

	A:   1--2--4
	     \  |  /
	      --3-- 

#Q3 If you toss a fair coin 2000 times, what is the probability that you get exactly 1000 heads (and exactly 1000 tails)

	A: (2000 choose 1000)/(2^2000)

#Q4 If you roll a fair die 6000 times, what is the probability that each of the possiblie outcomes {1,2,3,4,5,6} occurs exactly 1000 times(23min)

	A: (6000 choose 1000)(5000 choose 1000)(4000 choose 1000)(3000 choose 1000)(2000 choose 1000)/6^6000

#Q5 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. Write the graph in our data Structure.

	A: {{2,3,4,5,6},{1,7,8,9,10,11},{1,12,13,14,15,16},{1,17,18,19,20,21},{1,22,23,24,25,26},{1,27,28,29,30,31},{2},{2},{2},{2},{2},{3},{3},{3},{3},{3},{4},{4},{4},{4},{4},{5},{5},{5},{5},{5},{6},{6},{6},{6},{6}}
	 					 
#Q6 Look at the cities that border piscataway, aand for each of them those that border them and again until you get to princeton
	(i) contruct the graph
	(ii) Find the number of paths from piscataway to pricenton
		(a) Find the actual set using Paths
		(a) By usin NuPaths
		(c) buy using GFt

	A:

	(i) {{franklin, New Brunswick, Highland Park, Edison, South Plainfield, Plainfield, Dunellen, middlesex, south bound},{bridgewater, hillsborough, naville, millstone, montgomery, rocky hill, southbound brook, pricenton, new brunswick, north brunswick, piscataway, south brunswick}, {piscataway, highland park, edison, north brunswick, eats brunswick, franklin}, {edison, New brunswick, piscataway},{east brunswick, highland park, new brunswick, piscataway, sayreville, south plainsfield, woodbridge township, clark, plainfield, scotch plains},{piscataway, edison, plainfield, scotch plains},{scotch plains, fanwood, south plainfield, piscataway, dunellen, edison, green brook, north plainfield, watchung},{middlesex, piscataway, green brook, somerset, plainfield},{ dunellen, piscataway, bound brook, bridgewater, green brook, south bound brook},{bound brook, bridgewater, franklin, middlesex, piscaraway}