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Question 1
Reproduce the proof that egf(c) = egf(a)*egf(b)

Answer 1
We start of by imagining two combinatorial families (that can be unrelated?) A and B, and there are a(n) labeled objects in A and b(n) labeled objects in b. We nwo try to create a new set C = A x B. 
So c(n) = sum(binomial(n, k)*a(k)*b(n-k), k =0..n)
We basically choose k objects from a b and make a label of them
We then multiply both sude by x^n/n! and sum them from n = 0 .. infinity

We get 
Egf(c) = Egf(A)*Egf(B)

Question 2
Using Maple or otherwise find the ordinary generating function and exponential generating function for
a(n)=n*(n-1)*(n-2) (n ≥ 0)

Answer 2
ordinary generating function: 6*x^3/(x - 1)^4
exponential generating function: x^3*exp(x)

Question 3
i) How many ordered pairs [SP1,SP2] are there where SP1 and SP2 are set partitions of different sets whose total numbers is 100 and the labels are {1, ..., 100}
(ii) How many sets {SP1,SP2} where SP1 and SP2 are set-partitions of different sets whose total numbers is 100 and the labels are {1, ..., 100} ?

[Reminder the egf of set-partitions is exp(exp(x)-1) ]


Answer 3
I know we have to use the fact that egf(A)= egf(B)*egf(c) but I don't know how to implememnt it