We have $25,000 that must be invested among 5 possible opportunities. Each investment must be integral in units of $1,000, and there are minimal investments that need to be made if one is to invest in these opportunities. The minimal investments are $2,000, $3,000, $3,000, $4,000 and $5,000. How many different investment strategies are available if (a) an investment must be made in each opportunity?
(b) investments must be made in at least 4 of the 5 opportunities?