> 
> #ATTENDANCE QUIZ FOR LECTURE 3 of Dr. Z.'s Math454(02) Rutgers University
> 
> # Please Edit this .txt page with Answers
> 
> #Email  ShaloshBEkhad@gmail.com 
> #Subject: p3
> #with an attachment called
> #p3FirstLast.txt
> #(e.g. p3DoronZeilberger.txt)
> 
> #Right after finishing watching the lecture but no later than Sept. 14, 2020, 8:00pm

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> #Q1. THE FIRST ATTENDANCE QUESTION WAS:

> #What is a derangement
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> 
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> #A1. MY ANSWER TO THE FIRST ATTENDANCE QUESTION IS:
> 
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> #a derangement is a permutation that has no fixed points.
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> 
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> #Q2. THE  SECOND ATTENDANCE QUESTION WAS:
> 
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> #Give two examples of WtoS and StoW
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> 
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> #A2. MY ANSWER TO THE  SECOND ATTENDANCE QUESTION IS:

> #WtoS(w): inputs a word in {0,1} outputs the correpsonding subset of {1,...,n} (where n=nops(w))
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> WtoS:=proc(w) local n,i,S:
> 
> n:=nops(w):
> 
> S:={}:
> 
> for i from 1 to n do
>  if w[i]=1 then
>   S:=S union {i}:
>  fi:
> od:
> 
> S:
> 
> end:

> WtoS([0,0,1])
{3}
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> #StoW(S,n): inputs a subset S of {1,...,n} and outputs the corresponding binary word
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> StoW:=proc(S,n) local i,w:
> 
> if S  minus {seq(i,i=1..n)}<>{} then
>  print(S, `is not a subset of`,  {seq(i,i=1..n)} ):
>  RETURN(FAIL):
> fi:
> 
> w:=[]:
> 
> for i from 1 to n do
>  
> if member(i,S) then
>   w:=[op(w),1]:
> else
>   w:=[op(w),0]:
> fi:
> 
> od:
> 
> w:
> 
> end:
> StoW({3,2,3},3)
[0, 1, 1]
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> 
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> #Q3. THE  THIRD ATTENDANCE QUESTION WAS:
> 
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> #PROVE THAT THE PERMUTATIONS OF [1,2,3,...,n] is n!
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> 
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> #A3. MY ANSWER TO THE  THIRD ATTENDANCE QUESTION IS:
> 
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> #For 1st we have n possibilities, for 2nd we have n-1 possibilities, for 3rd we have n-2 possibilities
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> #So the total is n*(n-1)*(n-1)*...*1, which is n!
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