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Problem.We have 20 thousand dollars that must be invested among 4 possible opportunities. Each investment must be integral in units of 1 thousand dollars, and there are minimal investments that need to be made if one is to invest in these opportunities. The minimal investments are 2, 2, 3, and 4 thousand dollars. How many different investment strategies are available if investments must be made in at least 3 of the 4 opportunities.

Answers.572

Attempt.Let a, b, c and d be the 4 possible opportunities with minimal investments of 2, 2, 3 and 4 thousand dollars respectively. The possible combinations of opportunities are abc, abd, acd and abcd right? Now, would it illegal to invest 3 thousand dollars into opportunity a? Must it be multiples of 2 thousand? Ditto for the rest of the opportunities.

If it has to be in multiples of the minimum investment, how would one count them effectively? All I can think of doing is writing down combinations and looking for patterns.

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# Homework Help: Funky Counting Question

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