#OK to post homework
#Hari Amoor, November 15, 2020, Homework Assn. #19

# Question 1

# Let A and B be two distinct families of labeled objects, where there are a(n) labeled objects of size n in A and b(n) labeled objects of size n in B.  

# Spse. A, B are distinct families of labeled objects containing a(n) and b(n) labeled objects of size n respectively. We arrive at the conclusion that
# c(n) for C = A X B is equal to sum(binom(n,k)*a(k)*b(n-k), k=0..n). Similarly, we arrive at the conclusion that EGF(C) = EGF(A X B) = EGF(A)EGF(B).

# Question 2

# sum(x^n*n*(n-1)*(n-2)/n!,n=0..infinity)  =  x^3*exp(x)

# Question 3

# We supply the following:

# coeff(taylor(exp(exp(x)-1)*exp(exp(x)-1),x=0,101),x,100)*100! =
# 86635961604145793709294621186421021577187015751602637085427283871117865337554218116225569701173834817160231371909161518471870 ordered pairs

# coeff(taylor(exp(exp(x)-1)^2/2!,x=0,101),x,100)*100! =
# 43317980802072896854647310593210510788593507875801318542713641935558932668777109058112784850586917408580115685954580759235935 sets