#ATTENDANCE QUIZ FOR LECTURE 2 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p2
#with an attachment called
#p2FirstLast.txt
#(e.g. p2DoronZeilberger.txt)

#Right after finishing watching the Second lecture but no later than Friday, Sept. 11, 2020, 8:00pm




Q1. THE FIRST ATTENDANCE QUESTION WAS:

#Let a:=FIRST DIGIT of your RUID
#Let b:=SECOND DIGIT of your RUID
#Let c:=FIFTH DIGIT of your RUID
#Let d:=SIXTH DIGIT of your RUID
#HOW MANY WALKS IN MANHATTAN ARE THERE (NOT USING BDWAY)
#From CORNER of min(a,b) St and min(c,d) Ave
#to CORNER of max(a,b) St and max(c,d) Ave
#Walking in the positive direction


A1. MY ANSWER TO THE FIRST ATTENDANCE QUESTION IS:

My RUID: 193006310
a=1,b=9,c=0,d=6

Rephrased question:
How many walks in Manhattan are there (not using Broadway) from corner of 1st St and 0th Ave
to the corner of 9th St and 6th Ave walking in the positive direction?

Streets run east and west, Avenues run north and south

Must walk 8 blocks north, 6 blocks east

There are (8+6)!/(8!6!) = 14!/(8!6!) = 3003 walks from corner of 1st St and 0th Ave 
to the corner of 9th St and 6th Ave only walking in the positive direction.




Q2. THE  SECOND ATTENDANCE QUESTION WAS:

#CONSIDER YOUR RUID AS A WORD of LENGTH 9 in
#THE 10-letter "ALPHABET" {0,1,2,...,9}
#HOW MANY WAYS TO REARRANGE YOUR RUID?


A2. MY ANSWER TO THE  SECOND ATTENDANCE QUESTION IS:

My RUID: 193006310
There are three 0's, two 1's, two 3's, one 6, and one 9.
In total, there are (3+2+2+1+1)!/(3!2!2!1!1!) = 15,120 rearrangements of the numbers of my RUID.