#Generating_Function

Question

We are interested in generating functions for the number of different ways to com­
pose a bag of n donuts subject to various restrictions. For each of the restrictions
in  below, find a closed form for the corresponding generating function.

1.The donuts must be chocolate, glazed, coconut, or plain and:
       • there must be at least 3 chocolate donuts, and
       • there must be at most 2 glazed, and
       • there must be exactly 0 or 2 coconut, and
       • there must be a multiple of 4 plain.

2.  All the donuts are plain and their number is a multiple of 4

Comments

My approach for 1^st part -

For choclate (at least 3) :- x³+x⁴+x⁵ +x⁶ +.......

For glazed donuts (at most two) :- 1+x+x²

for doconut donut (exactly 0 or 2) :- 1+x²

For plain Donut (multiple of 4) :- x⁴ +x⁸ +x¹² +........

But after this how to combine all the 4 function I don't know. Someone please help

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take their product.