Question 3: Assume we wish to compose a bag of n fruits subject to the following constraints: (i) We may use at most 6 apples. (ii) Any number of oranges divisible by 3 may be used. There are no other types of fruit available. (a) Determine the generating function for each of the 2 conditions in a closed form. (b) From the previous result compose the generating function of the given counting problem. (c) Expand the generating function resulting from (b) in order to derive a general formula for the problem in question.
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We can use any number of oranges that are divisible by 3, so the generating function is: f(n) = 6n + 3 Show more…
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